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curve #4418

y² + y = x³ − x² − 18219470x + 19461310622

a-invariants: [0, -1, 1, -18219470, 19461310622]
c-invariants: [874534576, -16809325170200]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 74517748861467542239239
discriminant (Δ): 223553246584402626717717
Faltings height: 3.1829
naive height: 61.7676
primes of bad reduction: 3, 359, 7351, 16493, 570686950049
regulator: 8778980.71623037483319190296009056315644763822773671788866275
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:04 UTC
last updated: 2026-10-17 10:23:04 UTC

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

(-4651, 59740)
(-3508, 200482)
(-2482, 222229)
(-1933, 217837)
(-895, 187216)
(3611, 27253)
(4253, 137419)
(4367, 152182)
(4586, 179821)
(5276, 264898)
(5368, 276245)

Commentary

BASE records/rank_11.md#15 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:04 UTC · history

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