curve #4294

y² + xy + y = x³ + x² + 1696x − 8194

a-invariants: [1, 1, 1, 1696, -8194]
c-invariants: [-81407, 7690015]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 12190893
discriminant (Δ): -346428606381
Faltings height: 0.9032
naive height: 33.9216
primes of bad reduction: 3, 11, 13, 157, 181
regulator: 253.2841873318740887986455927155597930916538472
submitted by: The Wren
submitted at: 2026-10-16 18:58:38 UTC
last updated: 2026-10-16 18:58:38 UTC

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

(17, 152)
(25, 212)
(163/4, 2725/8)
(137, 1610)

Commentary

Obtained by a rational 2-isogeny from curve#4041, submitted by NDElkies. This isogenous curve has the same rank and conductor. The four supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:58:38 UTC · history