curve #4617

y² + xy + y = x³ + x² − 248916753995846346986951734789610765x + 25215283086543121974458620542320082052072209277074947

a-invariants: [1, 1, 1, -248916753995846346986951734789610765, 25215283086543121974458620542320082052072209277074947]
c-invariants: [11948004191800624655373683269901316721, -21786004586773257475542279587069235808293013339652629769]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 13178037168409810631180244256476178872980088517494507510
discriminant (Δ): 712387154360819796158835846389407734382110032816885376573735185903066456287635494546612158516161059151360000
Faltings height: 19.3921
naive height: 256.1209
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 37, 43, 47, 89, 101, 103, 127, 149, 191, 223, 227, 307, 571, 577, 647, 701, 1019, 1193, 171179
regulator: 3272593048440232.023543623454539336324465295071537617127990300137028781
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:25:41 UTC
last updated: 2026-10-19 03:25:41 UTC

(96720921990485105391475687/8972067841, -127570378476237170140227674691929874530444/849843237967361)
(-60534043352866393, 200153444935036570644670196)
(2821607316470507, 156566152842721773213977996)
(12104922564576887, -149009861352257781883171564)
(-676153255183028067616092509030153/1245036235475041, 657113498873108930085082905741129422444472473516/43931191966309540412911)
(-2348200791270849630206378073484433/4407997385348001, 23849573359218353338511725112971007370964313055956/292659072814060878740751)
(-347502133542016213, -264103798320530646809431864)
(-464493318135207433, -201541908423887534085824524)
(58614523920532660543/49, -411479465793889883983557660772/343)
(-924979104340194736685887370920920314437/3985179740429892721369, 66791801865065747422919259508327661725849708279386948404848/251577542651637238480450246010653)
(706958940681015977, 450081141843051712643569156)
(29215318299889906075/36, 129181994259404116529628453803/216)
(-7909308326431358512520556197603241569/47421801571939447041, 81373585413119654654406124843697130871908426621114219556/326563072466175727583642569089)
(-1344197525088030604176833/153239641, 313990633834908434583409522233939052604/1896953515939)
(-269010928700742487573/841, 6549170281893457041129031611724/24389)
(-126795466341274309, -233962169591320703146485076)

X400, T=-2357/2646.

last edited by Andrii Prokhorenkov at 2026-10-19 03:25:41 UTC · history