curve #4109

y² + xy = x³ − 245761852825943276490812536359166198563131230504891x + 1480028475895726460167494910888419741421146150726328849110625607928121665425

a-invariants: [1, 0, 0, -245761852825943276490812536359166198563131230504891, 1480028475895726460167494910888419741421146150726328849110625607928121665425]
c-invariants: [11796568935645277271559001745239977531030299064234769, -1278744603173907661584715620702448060055786181566050743491546821795345715279353]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 1213249524563722385101574358389528895083959754877740265336233395688563597023994735590
discriminant (Δ): 3710319645215116882931334093806679722449858066679895155028589198538731481291401839522430576374234260650442983471120829457545858613147155758213623360000
Faltings height: 27.7734
naive height: 359.6989
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 59, 67, 71, 73, 79, 107, 137, 163, 593, 659, 929, 4903, 8821, 9431, 10369, 55343, 381739, 414737, 565891, 678553, 1639459
regulator: 18213594436607546135466.6253825752304024232600212584432159860491792143809722189
submitted by: wgxli
submitted at: 2026-10-09 15:24:30 UTC
last updated: 2026-10-09 15:24:30 UTC

(8707009562613300220280978, 523084446572979876888365622336684761)
(7259318381029930633138784, 8860832180952679331343024754130919401)
(7746088951278928839143078, 6412122235467020674019973070674434561)
(8205593740486767718607528, 3987943572201676428516513885016187711)
(8556756984083639757326278, 1900902154030947160595480799423843961)
(9570050402000654156168150, 2134595681122076149106093203335174305)
(9739090214833576926404726, 3206733640064966965492047726292012385)
(2830992024531796679457134, 28407176224383063312009812265031768001)
(3059934620147458073739278, 27507527216906141416393382913224188961)
(3414616532490923812890578, 26089443723638505428848446470020859861)
(4233242966170464495421550, 22705065949431477413542708914028387025)
(-3682222477103899617796972, 48322374888062926868030240451845358011)
(-6439478773166185751178706, 52873259523446249163816370771552582145)
(15641315453872912939881578, 38244598997071560560104472029030403561)
(16656728388417478293185384, 44808400035203021848603923911335919615)
(20946149558338297030049144, 74311522338087993214720327679977863695)
(34274736736586854899700778, 182540714357273858849790302722663302761)
(234576628106553230470114934/25, 45413298520860184574034678010953561013/125)
(601632552608080409710442225/64, 347592008680675367102930958565428250285/512)
(45201035697475209077162089712/5329, 929223602532653345197994593466265550175087/389017)

2-isogenous to curve #4108

last edited by wgxli at 2026-10-09 15:24:30 UTC · history