Several issues for n=2 and d=3

[edgarcosta]

R.<x,y,z> = QQ[]
f = x^3 + y^3 + z^3
for p in prime_range(4, 1000):
    f1 = controlledreduction(f, p)
    f2 = EllipticCurve(f, [1,-1,0]).change_ring(GF(p)).frobenius_polynomial().reverse()
    if f1.list() != f2.list():
        print(p, f1.list(), f2.list())
        
19 [1, 3, 19] [1, 7, 19]
31 [1, 14, 29822] [1, 4, 31]
37 [1, 10, 37] [1, -11, 37]
43 [1, -10, 43] [1, -8, 43]
61 [1, 0, 61] [1, 1, 61]
67 [1, 0, 67] [1, -5, 67]
73 [1, -9, 73] [1, 7, 73]
79 [1, 24, 493118] [1, -17, 79]
97 [1, 0, 97] [1, 19, 97]
103 [1, 54, 1092830] [1, 13, 103]
109 [1, -15, 109] [1, -2, 109]
127 [1, 66, 2048510] [1, -20, 127]
139 [1, 105, 2685758] [1, -23, 139]
151 [1, 0, 151] [1, 19, 151]
157 [1, 0, 157] [1, -14, 157]
163 [1, 0, 163] [1, 25, 163]
181 [1, 0, 181] [1, 7, 181]
193 [1, 135, 7189250] [1, -23, 193]
199 [1, 128, 7880798] [1, -11, 199]
211 [1, 162, 9394142] [1, 13, 211]
223 [1, 0, 223] [1, 28, 223]
229 [1, 186, 12009218] [1, 22, 229]
241 [1, 182, 13997762] [1, -17, 241]
271 [1, 0, 271] [1, -29, 271]
277 [1, 86, 21254210] [1, -26, 277]
283 [1, 0, 283] [1, -32, 283]
307 [1, 196, 28934750] [1, 16, 307]
313 [1, 133, 30664610] [1, -35, 313]
331 [1, -12, 331] [1, 1, 331]
337 [1, 168, 38273090] [1, -5, 337]
349 [1, 247, 42508898] [1, 37, 349]
367 [1, 303, 49431230] [1, -35, 367]
373 [1, 0, 373] [1, 13, 373]
379 [1, 0, 379] [1, -29, 379]
397 [1, 176, 62571170] [1, 34, 397]
409 [1, 19, 409] [1, 31, 409]
421 [1, 255, 74618882] [1, 19, 421]
433 [1, 322, 81183170] [1, -2, 433]
439 [1, 275, 84604958] [1, 28, 439]
457 [1, 59, 95444450] [1, 10, 457]
463 [1, 67, 99253310] [1, -23, 463]
487 [1, 3, 487] [1, 25, 487]
499 [1, 354, 124251998] [1, -32, 499]
523 [1, -22, 523] [1, 43, 523]
541 [1, 0, 541] [1, -29, 541]
547 [1, 64, 163667870] [1, 1, 547]
571 [1, -10, 571] [1, 31, 571]
577 [1, 436, 192100610] [1, -11, 577]
601 [1, 0, 601] [1, -26, 601]
607 [1, 0, 607] [1, 49, 607]
613 [1, 0, 613] [1, -47, 613]
619 [1, 115, 237177278] [1, -17, 619]
631 [1, 257, 251240222] [1, 43, 631]
643 [1, 561, 265848350] [1, 40, 643]
661 [1, 459, 288805442] [1, 49, 661]
673 [1, 188, 304821890] [1, 37, 673]
691 [1, 554, 329940062] [1, -8, 691]
709 [1, 455, 356401538] [1, -53, 709]
727 [1, 0, 727] [1, -44, 727]
733 [1, 0, 733] [1, -50, 733]
739 [1, 530, 403584158] [1, 16, 739]
751 [1, 156, 423565502] [1, -41, 751]
757 [1, 313, 433798850] [1, -29, 757]
769 [1, 211, 454757378] [1, 49, 769]
787 [1, 0, 787] [1, 31, 787]
811 [1, 211, 533412542] [1, -56, 811]
823 [1, 0, 823] [1, -5, 823]
829 [1, 0, 829] [1, 7, 829]
853 [1, 136, 620651330] [1, -35, 853]
859 [1, 85, 633840638] [1, 13, 859]
877 [1, 133, 674527010] [1, -59, 877]
883 [1, 798, 688466270] [1, -47, 883]
907 [1, 776, 746143550] [1, 19, 907]
919 [1, 135, 776152478] [1, 52, 919]
937 [1, 0, 937] [1, 61, 937]
967 [1, 354, 904232030] [1, -41, 967]
991 [1, -12, 991] [1, 61, 991]
997 [1, 921, 991027970] [1, 10, 997]