curve #4697

y² + xy + y = x³ + x² − 398200x + 95463896

a-invariants: [1, 1, 1, -398200, 95463896]
c-invariants: [19113601, -82624158305]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 1274102071359
discriminant (Δ): 90286695082712817
Faltings height: 2.0617
naive height: 50.2977
primes of bad reduction: 3, 13, 23, 79, 277, 4993
regulator: 687.71751322010434229809890105732808797503607590445
submitted by: The Wren
submitted at: 2026-10-20 20:50:28 UTC
last updated: 2026-10-20 20:50:28 UTC

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

(-632, 10072)
(694, 12061)
(-502, 13257)
(1292, 41064)
(1343, 43884)
(96, 7576)

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 20:50:29 UTC · history