curve #310

y² + xy = x³ − 1873940813132840352272936419410635778826863x + 987165421651192729341038595063275202627467898519141617381276217

a-invariants: [1, 0, 0, -1873940813132840352272936419410635778826863, 987165421651192729341038595063275202627467898519141617381276217]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 288223154151653778337307627146202434973670195623654112440970678577409850
naive height: 303.6235
Faltings height: 23.0216
discriminant (Δ): 178366552240819613635837756699513126037238421271340078083424114134861955668984171479187414542891604318460528025744022574000000
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 41, 43, 47, 73, 89, 131, 139, 239, 271, 353, 421, 541, 1093, 1213, 1559, 1597, 2137, 41863, 11763979, 120637667
regulator: 3009837047616775911933.4738366476941867198979824999142088194142052852
submitted by: 7fff-zip
submitted at: 2026-08-24 00:23:41 UTC
last updated: 2026-08-24 00:23:41 UTC

(799840690172437237002, -74124023837099984429314439151)
(946552773350163704952, 7839452045181737934246991070949)
(1023543498037633447502, 11891674387395523949955062395349)
(1099628437192474872702, 16005577042048616153244271649949)
(879487824228726276702, 4397737920903035833439489384349)
(350043944601632770928172/361, 62029368003638112435022913227339791/6859)
(221095394121209752211454/25, 102782873694821235326444692655063073/125)
(8124907327459805999504178/6241, 13538388180836629494681145414571072475/493039)
(756734090541992519954681418/908209, -1779530276693287296103600588532558258727/865523177)
(10763115065471324542089237/13456, 130978900453167288482275185537941829/1560896)
(361954644813292998523643866/245025, 4606491180408297912452432294281927061551/121287375)
(264926877915557975880310362/120409, 3622119185007435719725154657671158214515/41781923)
(21457014281338063318584153543/21883684, 984062953116997581219421549296878808940323/102371873752)
(19997257543170685695047316942/57121, 2827823795355781016676779453965880226484731/13651919)
(7300917094470207583721526208/31329, 623819073291871596803504084788826391255067/5545233)

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