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curve #4379

y² = x³ − x² − 284743456964x + 58481641844921604

a-invariants: [0, -1, 0, -284743456964, 58481641844921604]
c-invariants: [13667685934288, -50528056547896660160]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 24863086248
discriminant (Δ): 67305174902942076402707455674624
Faltings height: 5.2129
naive height: 90.7382
primes of bad reduction: 2, 3, 7, 11, 13, 37, 83, 337
regulator: 8483.206756019629049511093124385615116406070914
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:53 UTC
last updated: 2026-10-17 10:06:53 UTC

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

(7685890/9, 17871524216/27)
(16055250/49, 6511173864/343)
(128277085/324, -515292553009/5832)
(52941441970/136161, 4065959364797512/50243409)

Commentary

2-ISOG#1 torsion/torsion_Z4.tsv.gz:352 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:53 UTC · history

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