curve #1094

y² + xy = x³ − 3871874529581532682991685x + 2932443695831973034287157248711276225

a-invariants: [1, 0, 0, -3871874529581532682991685, 2932443695831973034287157248711276225]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 363617817781788570 ☆ record for ℤ/7ℤ torsion, rank ≥ 5
discriminant (Δ): 5890016282309990838050424070535904910400357804209544486868391680000000 ☆ record for ℤ/7ℤ torsion, rank ≥ 5
Faltings height: 12.6851 ☆ record for ℤ/7ℤ torsion, rank ≥ 5
naive height: 181.4609 ☆ record for ℤ/7ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 109, 3079, 65479
regulator: 7487.00296361143571087481253403437183875810577656
submitted by: dujella
submitted at: 2026-09-23 18:38:53 UTC
last updated: 2026-09-23 18:38:53 UTC

(1139468193570, 6113353595217015)
(423997075362, 1169189107911863031)
(1157854869570, 40341192423477015)
(1137065493270, 1069297314954015)
(1137272072370, 1646036791995015)

found by Dujella - Kulesz (2001)

last edited by dujella at 2026-09-23 18:38:53 UTC · history