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curve #4416

y² + y = x³ − 15834277x − 1218408864

a-invariants: [0, 0, 1, -15834277, -1218408864]
c-invariants: [760045296, 1052705258280]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 253441148857651353024037
discriminant (Δ): 253441148857651353024037
Faltings height: 3.1803
naive height: 61.3467
primes of bad reduction: 10451402411, 24249487187567
regulator: 14916379.5274969770593584772736770676244041543595898088404778
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:59 UTC
last updated: 2026-10-17 10:22:59 UTC

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

(-3938, 8190)
(-3932, 15836)
(-3661, 87651)
(-3269, 124940)
(-2371, 151643)
(-2354, 151694)
(-2167, 151388)
(-1722, 144713)
(-1094, 121634)
(4065, 39827)
(4571, 148019)

Commentary

BASE records/rank_11.md#12 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:59 UTC · history

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