curve #4290

y² + xy = x³ + x² + 3310150588x + 448339751053770

a-invariants: [1, 1, 0, 3310150588, 448339751053770]
c-invariants: [-158887228199, -387364353256245725]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 19601750875338708054
discriminant (Δ): -89156408730746321217792923255058
Faltings height: 4.8109
naive height: 80.9963
primes of bad reduction: 2, 3, 11, 17, 19, 23, 167, 577, 7297, 56857
regulator: 52068503.001612203965757807298962239408943858157121797985
submitted by: The Wren
submitted at: 2026-10-16 18:52:00 UTC
last updated: 2026-10-16 18:52:00 UTC

Witness: 9 independent points log in to add more points →

(21489, 22997847)
(6061, -21650785)
(-20501, 19293987)
(-43139, -14987260)
(-553919/9, 92309053/27)
(257659/4, 243557485/8)
(219109, 108023852)
(78679, 34541582)
(-62301, -519213)

Commentary

Obtained by a rational 2-isogeny from curve#4057, submitted by NDElkies. This isogenous curve has the same rank and conductor. The nine supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:52:00 UTC · history