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curve #4477

y² + xy + y = x³ − 9494793x + 36701246672

a-invariants: [1, 0, 1, -9494793, 36701246672]
c-invariants: [455750041, -31710560749885]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 263569643529999464027834
discriminant (Δ): -527139287059998928055668
Faltings height: 3.2358
naive height: 62.1753
primes of bad reduction: 2, 1256863, 104852177019293059
regulator: 13920406.1177610490122251450412991013422407666074027642816493
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:43 UTC
last updated: 2026-10-17 10:30:43 UTC

Witness: 11 independent points log in to add more points →

(-451, 202442)
(-4115, 80136)
(1211, 163648)
(3497, -216844)
(-4219, 42928)
(-1103, -213534)
(4363/4, -1334457/8)
(1333, -163190)
(4459, 285912)
(-2981, -194768)
(-3010, -193462)

Commentary

BASE records/rank_11.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:43 UTC · history

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