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curve #4422

y² + y = x³ − 1628809x + 524691642

a-invariants: [0, 0, 1, -1628809, 524691642]
c-invariants: [78182832, -453333578904]
rank (lower bound): ≥ 10
torsion subgroup: trivial
conductor (N): 157630523181786606709
discriminant (Δ): 157630523181786606709
Faltings height: 2.5785
naive height: 54.5237
primes of bad reduction: 100483, 1568728274253223
regulator: 1063358.227780077106108989798872008262353936260512535040576
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:15 UTC
last updated: 2026-10-17 10:23:15 UTC

Witness: 10 independent points log in to add more points →

(-1171, 28745)
(-822, 36168)
(-681, 36305)
(-560, 35513)
(-427, 33798)
(-152, 27726)
(245, 11846)
(345, 1953)
(1089, 6510)
(1107, 8841)

Commentary

BASE records/rank_10.md#12 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:15 UTC · history

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