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curve #4503

y² + xy = x³ + x² − 8641115852x + 118070298518460

a-invariants: [1, 1, 0, -8641115852, 118070298518460]
c-invariants: [414773560921, -102015848721656285]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 132695994717361298982
discriminant (Δ): 35271533578584820136881378371012
Faltings height: 4.7465
naive height: 80.2530
primes of bad reduction: 2, 3, 11, 47, 73, 89, 97, 109, 401, 17449
regulator: 190705.12963305616773210426614891537221939208477426598929
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:44 UTC
last updated: 2026-10-17 10:32:44 UTC

Witness: 9 independent points log in to add more points →

(89462, 7767656)
(-42373, 20223737)
(227402, 99447662)
(-73547, 18898842)
(-44493, -20336103)
(3372929, 6190536017)
(13001, 2808614)
(-32033, 19042392)
(4239589/9, 8556450790/27)

Commentary

BASE torsion/torsion_Z2.tsv.gz:644933 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:44 UTC · history

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