Exec error when writing ELF64 from scratch

Question

I'm trying to learn about the elf standard by writing an elf executable from scratch. Elf32 didn't pose much of a problem, using this code:

BITS 32

            org     0x08048000

ehdr:                                                 ; Elf32_Ehdr
            db      0x7F, "ELF", 1, 1, 1, 2         ;   e_ident
    times 8 db      0
            dw      2                               ;   e_type
            dw      3                               ;   e_machine
            dd      1                               ;   e_version
            dd      _start                          ;   e_entry
            dd      phdr - $$                       ;   e_phoff
            dd      0                               ;   e_shoff
            dd      0                               ;   e_flags
            dw      ehdrsize                        ;   e_ehsize
            dw      phdrsize                        ;   e_phentsize
            dw      1                               ;   e_phnum
            dw      0                               ;   e_shentsize
            dw      0                               ;   e_shnum
            dw      0                               ;   e_shstrndx

ehdrsize      equ     $ - ehdr

phdr:                                                 ; Elf32_Phdr
            dd      1                               ;   p_type
            dd      0                               ;   p_offset
            dd      $$                              ;   p_vaddr
            dd      $$                              ;   p_paddr
            dd      filesize                        ;   p_filesz
            dd      filesize                        ;   p_memsz
            dd      5                               ;   p_flags
            dd      0x1000                          ;   p_align

phdrsize      equ     $ - phdr

_start:
            mov     bl, 42
            xor     eax, eax
            inc     eax
            int     0x80

filesize      equ     $ - $$

Source: http://www.muppetlabs.com/~breadbox/software/tiny/teensy.html

I can assemble this into an executable with nasm and it executes just fine:

$ nasm -f bin -o test32 template32.asm
$ chmod +x test32
$ ./test32 ; echo $?
42

Next, I tried to do the same with 64 bits. I've read the differences that I found here: https://www.uclibc.org/docs/elf-64-gen.pdf

Here is the result of the modifications I implemented:

BITS 64

            org     0x08048000

ehdr:                                                 ; Elf64_Ehdr
            db      0x7F, "ELF", 2, 1, 1, 2         ;   e_ident
    times 7 db      0
            db      0x10                            ;   e_nindent
            dw      2                               ;   e_type
            dw      3                               ;   e_machine
            dd      1                               ;   e_version
            dq      _start                          ;   e_entry
            dq      phdr - $$                       ;   e_phoff
            dq      0                               ;   e_shoff
            dd      0                               ;   e_flags
            dw      ehdrsize                        ;   e_ehsize
            dw      phdrsize                        ;   e_phentsize
            dw      1                               ;   e_phnum
            dw      0                               ;   e_shentsize
            dw      0                               ;   e_shnum
            dw      0                               ;   e_shstrndx

ehdrsize      equ     $ - ehdr

phdr:                                                 ; Elf64_Phdr
            dd      1                               ;   p_type
            dd      5                               ;   p_flags
            dq      0                               ;   p_offset
            dq      $$                              ;   p_vaddr
            dq      $$                              ;   p_paddr
            dq      filesize                        ;   p_filesz
            dq      filesize                        ;   p_memsz
            dq      0x1000                          ;   p_align

phdrsize      equ     $ - phdr

_start:
        mov     bl, 42
        xor     eax, eax
        inc     eax
        int     0x80

filesize      equ     $ - $$

Using the same commands as above, I get this error:

./test64: cannot execute binary file: Exec format error

Something I noticed: When calling file on both test32 and test64, I get a message telling me that the section header size is corrupted. I find that weird because I don't have any section header... I've also looked at each files with 010 editor and an ELF template but everything looks fine to me.

EDIT:

32bit hex dump:

7f45 4c46 0101 0102 0000 0000 0000 0000
0200 0300 0100 0000 5480 0408 3400 0000
0000 0000 0000 0000 3400 2000 0100 0000
0000 0000 0100 0000 0000 0000 0080 0408
0080 0408 5b00 0000 5b00 0000 0500 0000
0010 0000 b32a 31c0 40cd 80

64 bit hex dump:

7f45 4c46 0201 0102 0000 0000 0000 0010
0200 0300 0100 0000 7880 0408 0000 0000
4000 0000 0000 0000 0000 0000 0000 0000
0000 0000 4000 3800 0100 0000 0000 0000
0100 0000 0500 0000 0000 0000 0000 0000
0080 0408 0000 0000 0080 0408 0000 0000
8000 0000 0000 0000 8000 0000 0000 0000
0010 0000 0000 0000 b32a 31c0 ffc0 cd80

Answer 1

dw 3 ; e_machine

As per the System V Application Binary Interface AMD64 Architecture Processor Supplement that value should instead be 62 for Advanced Micro Devices X86-64. With that change, it runs for me.