curve #1994

y² + xy = x³ + 6848212831855708468163388684090085x + 445716096915199533261574703050462937323192786710225

a-invariants: [1, 0, 0, 6848212831855708468163388684090085, 445716096915199533261574703050462937323192786710225]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 6580537988822228363790 ☆ record for ℤ/10ℤ torsion, rank ≥ 4
discriminant (Δ): -106377073857377932650601307731885540389396382116262706994380254441099502911789666644459375000000000000000
Faltings height: 18.6442
naive height: 246.7707
primes of bad reduction: 2, 3, 5, 11, 13, 19, 31, 41, 43, 109, 113, 2251, 53279
regulator: 571859.8190700782133368120533541547143722903713
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:30:42 UTC
last updated: 2026-09-26 04:30:42 UTC

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

(11528418095716319830/81, 47822947995625980514265623265/729)
(8144897055127278694630/175561, -2161319990888351372389578504543685/73560059)
(-11493584603914736324930/237169, -19207800459130081736048559793145/115501303)
(20268782729270270551048033728321818080/76201652840122044481, 96592500114384720453727339855744138062844781602810121015/665191340875320717259173740129)

Commentary

New curve, 2-isogenous partner of curve#1090; the 4 witness points are transported through the rational isogeny and certified independent by the exact 2-descent character test.

last edited by Steps Unbounded at 2026-09-26 04:30:42 UTC · history