curve #2823

y² = x³ + x² − 13766104889980x + 17985682559929256228

a-invariants: [0, 1, 0, -13766104889980, 17985682559929256228]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 16804238845740
discriminant (Δ): 27214797469729973331075006622082076000000
Faltings height: 6.4969
naive height: 102.3733
primes of bad reduction: 2, 3, 5, 19, 61, 109, 241, 9199
regulator: 2481.30125823846221413258617894477540762216758632
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:03 UTC
last updated: 2026-09-26 20:24:03 UTC

Witness: 5 independent points log in to add more points →

(1534851104/529, -19119159779850/12167)
(865221029/4, -25446443220225/8)
(138256911476/151321, 146223966948774390/58863869)
(-2512924, 6058901250)
(97560392561/4096, -30121197199979145/262144)

Commentary

2-isogenous to curve#1666 via the rational 2-torsion point x=-1316976. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:03 UTC · history