curve #106

y² = x³ − 77547091492x + 6455011172238820

a-invariants: [0, 0, 0, -77547091492, 6455011172238820]
c-invariants: [3722260391616, -5577129652814340480]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 2299130784996838096010931135016
discriminant (Δ): 11845121804303709870648317207602432
Faltings height: 5.2504
naive height: 86.8361
primes of bad reduction: 2, 7, 23, 809, 301831, 2630231441, 2779338763
regulator: 9909246672.730008824881154639352039095879849904101177616705416006
submitted by: David Renshaw
submitted at: 2026-06-24 00:01:26 UTC
last updated: 2026-07-01 22:44:40 UTC

(-14090, 86861110)
(474, 80114006)
(80026, 27599402)
(92561, 8378233)
(231918, 30730714)
(273042, 75081338)
(273617, 75640537)
(303402, 104192438)
(343974, 143105494)
(533632, 342099562)
(1293552, 1438962938)
(2895824, 4905678694)
(3041382, 5282367062)

Found by Zev Klagsbrun.

last edited by David Renshaw at 2026-06-24 02:36:20 UTC · history