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curve #4478

y² + xy = x³ − x² − 108131509x + 432366460969

a-invariants: [1, -1, 0, -108131509, 432366460969]
c-invariants: [5190312441, -373541265871245]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 84065693672563262871566
discriminant (Δ): 168131387345126525743132
Faltings height: 3.3674
naive height: 67.1102
primes of bad reduction: 2, 42032846836281631435783
regulator: 7821720.07590037438720248030468500027162082139788193461204614
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:45 UTC
last updated: 2026-10-17 10:30:45 UTC

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

(-11692, 319227)
(4293, 215255)
(5260, 92793)
(22899/4, 221317/8)
(5792, 15795)
(5826, 7789)
(6440, 52083)
(6596, 74625)
(6812, 105403)
(7273, 171300)
(7283, 172740)

Commentary

BASE records/rank_11.md#39 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:45 UTC · history

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