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curve #4391

y² + xy + y = x³ + x² + 700175330673221x + 16719390490661090685920

a-invariants: [1, 1, 1, 700175330673221, 16719390490661090685920]
c-invariants: [-33608415872314607, -14445553131868063310275481]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 4272863122202808237
discriminant (Δ): -142728918967127538131307427114219227675994393743
Faltings height: 7.7309
naive height: 115.8649
primes of bad reduction: 3, 13, 17, 19, 23, 43, 101, 443, 883, 8681
regulator: 298688.5188767241844132542901485403420888769687432910
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:23 UTC
last updated: 2026-10-17 10:21:23 UTC

Witness: 7 independent points log in to add more points →

(2882906, 136972608711)
(153680135/4, 2533863529767/8)
(-20146726580/3249, 20404809902355500/185193)
(224516837/16, 10955988393279/64)
(29397634195/324, 5304024920189825/5832)
(14875181720/121, 1863665946216840/1331)
(2456321870384/63001, 5081760026469428208/15813251)

Commentary

BASE records/family_Z4.md#30 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:24 UTC · history

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