curve #1961

y² + xy + y = x³ − x² − 142096910387663238639176697x + 550038317971150796773537253808850944921

a-invariants: [1, -1, 1, -142096910387663238639176697, 550038317971150796773537253808850944921]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 177607531599020359811307295591679202791520350147804852864410
discriminant (Δ): 52927666180213562582728312417953848310983675587489682753837525862224293696000000
Faltings height: 14.0187
naive height: 192.2693
primes of bad reduction: 2, 5, 7, 13, 19, 29, 31, 37, 41, 725789, 1732043, 193281535595769391137786719851098799
regulator: 28276277713264184.10135669280204752463420545125628653819417739926459234621903
submitted by: Ritik Jain
submitted at: 2026-09-25 20:06:51 UTC
last updated: 2026-09-25 20:06:51 UTC

(239041706771419/4, 3626402426039224892477/8)
(9215360632831, 4812368158846165804)
(24864376424102035749016339/788911674849, -115944763389660657690633865742197508608/700716871982605743)
(151563568530211/36, -1110248263368923923381/216)
(145044276154501/16, 167712508760187796941/64)
(36850468894391, -212967280833749508916)
(13549431088611, 33349754097973521744)
(-575554536621919/256, 119988679601705180284169/4096)
(1447105561480771/121, -31531161358214462768316/1331)
(2725851197962494309/237169, -2409222508025051841401286768/115501303)
(37066699455635301/1681, -6217452455379722749705046/68921)
(8999350710831, -317211973116210196)
(168662423157251911/676, 69189303219224796940623819/17576)
(19149531578511, 69650328477539976044)
(459889947613109039/38809, 176046231392742603622540892/7645373)
(-119595998482592935401/660644209, 407446623870896486541738793268788/16980538103927)
(18150192019163945920039/1169161249, 1825598880046035997633048464646508/39977130587057)
(-81424477657540460176041/21072296569, 98714203944256413582296402462574468/3058917786845747)
(-831032813387018452173721/72163688689, 497725515704182219075304181589203628/19385548183592137)

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