curve #4611

y² + xy = x³ + x² − 9682089825240363517751292x + 11586062042591897085329683155674638800

a-invariants: [1, 1, 0, -9682089825240363517751292, 11586062042591897085329683155674638800]
c-invariants: [464740311611537448852062041, -10010357604802884634061932777369278388445]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 100584989890605528503345116207040193702
discriminant (Δ): 97804581689048611662037000394757934539656176821536579260864183586533247232
Faltings height: 13.1181
naive height: 184.2106
primes of bad reduction: 2, 3, 7, 11, 17, 19, 29, 31, 47, 61, 89, 179, 181, 397, 503, 601, 743, 787, 887
regulator: 9236489856.296976239905681774296445319093335389645860248563394892
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:23:15 UTC
last updated: 2026-10-19 03:23:15 UTC

(-3260438979096, 2914440056484353844)
(-1401691541304, 4733224461409116084)
(379321181864, 2822767733521265844)
(1543603225544, 564549683668615812)
(1701400072857, 195197356204089882)
(1874268658824, 152678630784142644)
(2413363945848, 1508598406615221060)
(2430654186984, 1553301303953000244)
(25127679359176, 125035666922782373764)
(58524164073811/36, 81538722779677349999/216)
(16550115944968/9, 66552848744326652/27)
(385686109735096/225, 546321343753449404636/3375)
(1546102681658824/729, 15136846067994350659100/19683)

X660, T=135/64.

last edited by Andrii Prokhorenkov at 2026-10-19 03:23:15 UTC · history