curve #740

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y² = x³ + x² − 1876514960051370952771328455345875345x + 996232844888856511706370313154494973861484579826900659

a-invariants

[0, 1, 0, -1876514960051370952771328455345875345, 996232844888856511706370313154494973861484579826900659]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

187901714216302676021769645984029439537718367054640275237726242655789730942983294186228280324216

naive height

262.1948

Faltings height

19.6984

discriminant (Δ)

-5852884199041382868082780323692733700277473128245666974828927335088734735924033137454296118643965071991153408

primes of bad reduction

2, 3, 7, 11, 23, 31, 67, 4339, 958040459612347226333, 512024735815866045820143363425125761451996287228966699120812621

regulator

13964752787095791868817132.8583952400954759624566580368277804610265563795522544093243

submitted by

Valery Asiryan

submitted at

2026-09-16 17:47:09 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-16 17:51:42 UTC

Witness: 23 independent points log in to add more points →

(-1443418125444959805, -835182951885003650781926778)
(-1282590205473960885, -1137155835653624574019771578)
(422431783868370551, -528124652297211250001993646)
(3528278996364503468109/5476, -94728033836414594771191615957917/405224)
(696221841123768567, -165039914698544974028808786)
(700495834440957051, -159597384519940815923998854)
(740702683679578815, -112572835384765537862003922)
(746126041858650387, -107180080921369210011426246)
(812269154804842383, -88980478870672709468635410)
(369613724498099016595/441, -1023870904555974952476447796942/9261)
(841989032332375851, -114683001256933635804934854)
(865708791999237267, -143262983297106899119058886)
(1018437935840035749357/1156, -6436954082628779117010523734429/39304)
(933758235501735270, -241183541166694817953147347)
(2525115478998008985, -3515462679515889783963296322)
(4161433846524722691, -8077933050022980537730488954)
(6885213370732771239, -17733515596166946494521495662)
(744578980583079291353/16, -20308603745188234445393006795355/64)
(70250306512642584825, -588695039136283448370743794722)
(75887590441619304942, -660976277012489475741454714161)
(280092894326521463030, -4687572014677199526056788162203)
(4468193218679028790966/9, -298673207688459676272480894542129/27)
(2691463897701994172986597083/24649, -139631318208109599061517252643595888662498/3869893)

Commentary

Specialization T=-47/23 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 23 listed points are certified independent by exact quadratic-character certificates.

last edited by Valery Asiryan at 2026-09-16 17:47:10 UTC · history