curve #5766

y² = x³ − 3655420843397482085295851167x + 73106004752467302900825469199428315987426

a-invariants: [0, 0, 0, -3655420843397482085295851167, 73106004752467302900825469199428315987426]
c-invariants: [175460200483079140094200856016, -63163588106131749706313205388306065013136064]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 147725718323159459649304740976684735669654367726596248934676752446916476440
discriminant (Δ): 817203901191885814833988896608922289250960996826757789481738326861097256018436000000
Faltings height: 14.8253
naive height: 202.0116
primes of bad reduction: 2, 5, 11, 47, 107, 15746089, 21669380992972142041, 195660244118793289143735029526857494722481
regulator: 3348200782649104524645.296160996042703137644979058171220975014416266569624767141724
submitted by: apkorte
submitted at: 2026-10-24 20:44:21 UTC
last updated: 2026-10-24 20:44:21 UTC

Witness: 22 independent points log in to add more points →

(10184974926677, 192177419055336664190)
(-19690833431383, -370741934635254336550)
(-66080356336933, -161586326778651539600)
(45587295403547, -34710815743475534080)
(-51300154463683, -354432986815932341350)
(113951217387117, 1065931154826673169450)
(15826509324457, 138627743910096207910)
(-16972568468783, 360913604731825646050)
(-187145058714287/9, 10107000286919187564770/27)
(-38809667806835, -395622203104345781386)
(66921707926447, -358034734274955941480)
(13259590808907673/289, 218283995659265808746870/4913)
(127703158241122857/196, 45444614332603463427828125/2744)
(90717367499117, -698618060523951281450)
(63087535843867, -305917063026743748800)
(17342567168757, -122178779448962623390)
(-65935950446805605/5041, 123300673959054290655122584/357911)
(-39525944473783, 394763944224354141050)
(282315751952497/16, 7599720987425403698825/64)
(-14400010516390, 350368538537896663334)
(-51859335746783, 351003826315231568050)
(127593185167753/9, -4194347066515250004250/27)

Commentary

Specialization at T = -5/12 of the rank-17 fibration of X1152 given in curve#3900. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-24 20:44:21 UTC · history