curve #5421

y² + y = x³ − 9241

a-invariants: [0, 0, 1, 0, -9241]
c-invariants: [0, 7984008]
rank (lower bound): ≥ 2
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 36963
discriminant (Δ): -36889110963
Faltings height: 0.7065
naive height: 31.7859
primes of bad reduction: 3, 37
regulator: 115.944829735749653984429244366576589408646
submitted by: The Wren
submitted at: 2026-10-21 22:45:57 UTC
last updated: 2026-10-21 22:45:57 UTC

Witness: 2 independent points log in to add more points →

(3097/144, -46819/1728)
(999001/900, 998485001/27000)

Commentary

Rational 3-isogeny partner of curve #3251: https://elliptic-rank.icarm.cloud/curve/3251 The source is Cremona 36963f1 = LMFDB 36963.g2: https://www.lmfdb.org/EllipticCurve/Q/36963/g/2 The two Cremona generators were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥2 is preserved under the rational isogeny. Rational torsion is trivial. This target is a cube-sum curve.

last edited by The Wren at 2026-10-21 22:45:57 UTC · history