curve #4007

y² + xy + y = x³ − x² + 6104710781312144316280654211323x + 353946714993848633126650315093497433178867991805

a-invariants: [1, -1, 1, 6104710781312144316280654211323, 353946714993848633126650315093497433178867991805]
c-invariants: [-293026117502982927181471402143519, -305809961754685220340043401004204954583163254565585]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 373194485014698697229027713931389442079902239969278
discriminant (Δ): -54134776153059133501420672633602124938975215355076407431250557480000984894622684760816771328252928
Faltings height: 17.4323
naive height: 232.4941
primes of bad reduction: 2, 3, 7, 11, 17, 19, 31, 37, 59, 109, 167, 181, 283, 983, 2221, 3163, 6563, 7867, 43117, 859378921
regulator: 1011444653885273516041.8784619964848407382891778214483828714801724055
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:44:28 UTC
last updated: 2026-10-05 04:44:28 UTC

Witness: 15 independent points log in to add more points →

(-441811123760373495883685/77986561, 255412220283973888047536833591682044/688699320191)
(54395050265588755583/121, 401186655358025562744874634552/1331)
(-197384667663581097665/66049, 9436003247033217309030157897312/16974593)
(2516095934557143239/3025, 99769506854052611501815044152/166375)
(193317138062976051103819/990025, 85006203628906580606182601176973188/985074875)
(167942349464404835591801831/105089430625, 20660219800609705684704722267572135508704/34067366172859375)
(-2036943370568251645487729/13536159025, 935719529788409734492377823417338858784/1574864421763625)
(20683222907054356904815/85544001, 471699677247995783524965814950694016/791196465249)
(362899264801456834825/10816, 6964148322268371914528852363641/1124864)
(10578883651569284352708295/60357361, 34412575677194298333897179289510097576/468916337609)
(12519753700662537506695/10452289, 20359023224574514400440598334121240/33792250337)
(63591086973100364818903/10201, 16035939427251734000060596694096512/1030301)
(-112148089910529154703725/39212644, 137396704272068338796450020603347107/245549576728)
(56030894639447366144255071/7154622225, 568369388941155889932685809820662866576/605173720901625)
(7873221415432301208162598056409117/119390001669987889, 699521021057457053923786238423325706396737786026258/41252658101398548913331287)

Commentary

Unlisted rational-isogeny neighbor of curve#3651 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:44:28 UTC · history