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curve #4368

y² + y = x³ − x² − 10693395740x + 422976559471818

a-invariants: [0, -1, 1, -10693395740, 422976559471818]
c-invariants: [513282995536, -365448667685677784]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 31150565605
discriminant (Δ): 970207476360225126363917753125
Faltings height: 4.5859
naive height: 80.8923
primes of bad reduction: 5, 31, 67, 223, 13451
regulator: 1185.013453499569272199063309274188439393844152
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:30 UTC
last updated: 2026-10-17 10:06:30 UTC

Witness: 4 independent points log in to add more points →

(-711, 20750402)
(1023316/9, 702546434/27)
(169135599/961, 1882416313637/29791)
(14773906691/16129, 1784754469989321/2048383)

Commentary

BASE families/family_Z5.tsv.gz:11 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:30 UTC · history

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