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curve #4472

y² + y = x³ + x² − 27593420x + 52869643590

a-invariants: [0, 1, 1, -27593420, 52869643590]
c-invariants: [1324484176, -45687318967000]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 136664518278987512577317
discriminant (Δ): 136664518278987512577317
Faltings height: 3.1926
naive height: 63.0129
primes of bad reduction: 7010513, 9932399, 1962690491
regulator: 14717135.8946309031224136839949856420571309141799994043409342
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:30 UTC
last updated: 2026-10-17 10:30:30 UTC

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

(-6014, 36566)
(-659/4, 1916847/8)
(1697, 104563)
(2215, 51209)
(2257, 45756)
(3596, 12541)
(3758, 47542)
(3802, 54153)
(4208, 106237)
(4707, 165218)
(5836, 301058)

Commentary

BASE records/rank_11.md#28 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

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

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