curve #4683

y² = x³ − x² − 7075875x + 7247021091

a-invariants: [0, -1, 0, -7075875, 7247021091]
c-invariants: [339642016, -6259388370560]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 2769734719104
discriminant (Δ): 22595495838450432
Faltings height: 2.4632
naive height: 58.9302
primes of bad reduction: 2, 3, 17, 41, 43, 59, 4079
regulator: 4631.2810045770810261403770065849199462601431736267
submitted by: The Wren
submitted at: 2026-10-20 20:37:10 UTC
last updated: 2026-10-20 20:37:10 UTC

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

(-2542, 93817)
(9695, 921854)
(21991/9, 1819234/27)
(1519, 1158)
(132655/81, 5082434/729)
(20513/16, 1072777/64)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the six supplied rational points exactly on this minimal model. The source records rank 6 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 20:37:10 UTC · history