curve #3826

y² + xy + y = x³ − 603025410331986472121182722690665497983x + 6002478554948352752158079389701076069682879626490561618806

a-invariants: [1, 0, 1, -603025410331986472121182722690665497983, 6002478554948352752158079389701076069682879626490561618806]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 383479070760315594490353206044733209331180103050379746028414611976674333108048598620320523070
discriminant (Δ): -1530678910296320686297479926452670851017965522490754078531805596486184844275818853665952742534252215386065676082812500
Faltings height: 21.2394
naive height: 279.6022
primes of bad reduction: 2, 3, 5, 7, 13, 23, 43, 59, 67, 83, 7621, 16481, 80151904175023021124695067929889413380293337856910907338417924871221683
regulator: 46859302033092467432842466.54876494967393515849936123422989457583626305438806592543134630
submitted by: 7fff-zip
submitted at: 2026-10-03 05:21:57 UTC
last updated: 2026-10-03 05:21:57 UTC

(-27698702760345034180, 38138603683525952638413317862)
(181136044891046490385/9, 1212983164309771234163970065884/27)
(16426948792522859465, 23007286033338217557076591842)
(-7553425766092488194290/289, -307181886465987163936065387559404/4913)
(-20055003226726500696160/841, 2014412150888929775105907980309313/24389)
(131394113947900544615, 1481624365862820524131126037442)
(11596497709362329365, -23853267863196754573020687058)
(14683819269712987415, -17714611897430015890564316358)
(1631292098134517249165/121, -23922882400673659680460213014198/1331)
(-1026886187281519600, 81367279497863338924654720482)
(2695564241601656995010/289, -169435909676026932101203287791379/4913)
(-22024169663229031060, -92738770645157166531607123683)
(11992088811145524865, -22260478390751300137703135308)
(3612562151193666740, -62218629881596639227593099058)
(31598914471101775747985/64, 5610237843292900228160596389481179/512)
(12074494790522135950, -21946145984593447865388054508)
(4983533300309214980, 55866361987237433161479558717)
(16228848886073018615, -22143894718642762694989389558)
(15361969818456638615, 19081232969098719344892072942)
(26754250296584608490, 94970564768927616697731159192)
(15099005464190666165, 18430011977675166628682028942)
(12505736455839663365, -20420991535443581673913738308)
(12489762258978337865, -20473508060004079898722374558)
(20719634751206987015, 49020599122893630876556883442)
(-16836497194456066435, -106689793767765274447487199258)

X1008; T=2989/927; 2-neighbor step: yes (Q has vector q=[-3,-1,1,3,0,2,1,1,2,-3,-1,2,-2,-2,1,1,1] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:21:58 UTC · history