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curve #4324

y² + xy + y = x³ − 1855258945632930x + 30757774810018365712880

a-invariants: [1, 0, 1, -1855258945632930, 30757774810018365712880]
c-invariants: [89052429390380617, -26574717569434512061499461]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 735700978777413923078
discriminant (Δ): -119754730679582092298744073834479139436
Faltings height: 7.1475
naive height: 117.0840
primes of bad reduction: 2, 7, 19, 73, 197, 373, 463, 769, 206879
regulator: 5746528.92214702317140607053185315600088255132131481684
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:04:51 UTC
last updated: 2026-10-17 10:04:51 UTC

Witness: 8 independent points log in to add more points →

(24868078, -10291763)
(25023905, 1335118555)
(24868275, -15343631)
(99574555/4, -1868485233/8)
(24863794, 24342753)
(24945302, -680121707)
(24871033, -38334713)
(227617363/9, 98532114113/27)

Commentary

BASE torsion/torsion_Z3.tsv.gz:7100 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:04:52 UTC · history

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