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curve #4340

y² + xy = x³ − 1247456750x + 19106431436932

a-invariants: [1, 0, 0, -1247456750, 19106431436932]
c-invariants: [59877924001, -16508046578395249]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 26752420782670
discriminant (Δ): -33467211796293389464768000000
Faltings height: 4.2020
naive height: 74.6852
primes of bad reduction: 2, 5, 11, 31, 41, 3457, 55351
regulator: 708.14665735111208298606117434815111582244091640229
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:29 UTC
last updated: 2026-10-17 10:05:29 UTC

Witness: 6 independent points log in to add more points →

(32354, 3535448)
(19972, 1459290)
(-30689/4, -42471551/8)
(-26276, 5822018)
(14314, 2038128)
(-191384/9, -161752714/27)

Commentary

BASE torsion/torsion_Z3.tsv.gz:490 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:29 UTC · history

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