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curve #4364

y² + xy = x³ − 527512126114350x + 4685195948378682480516

a-invariants: [1, 0, 0, -527512126114350, 4685195948378682480516]
c-invariants: [25320582053488801, -4048009337380054743399025]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 127432166671362
discriminant (Δ): -88279707243004626315174867839319172797431808
Faltings height: 7.2763
naive height: 113.3205
primes of bad reduction: 2, 3, 7, 19, 59, 67, 193, 209311
regulator: 2772.07230422376200810494283218900896680782327100
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:24 UTC
last updated: 2026-10-17 10:06:24 UTC

Witness: 5 independent points log in to add more points →

(49908980, 320406311714)
(19491516, 42515377218)
(31841338428/289, 5566884555940002/4913)
(12929268, 5110563618)
(-23953167054/1849, 7686355783138290/79507)

Commentary

BASE torsion/torsion_Z5.tsv.gz:1288 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:24 UTC · history

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