curve #2089

y² + xy + y = x³ + x² − 72385672634885161526x − 237022007538874673180581985197

a-invariants: [1, 1, 1, -72385672634885161526, -237022007538874673180581985197]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 274041685980626458099814310
discriminant (Δ): 4288029503079978793028476596063242015889659296532227649760
Faltings height: 10.0917
naive height: 148.7992
primes of bad reduction: 2, 3, 5, 13, 41, 83, 101, 157, 163, 313, 389, 409, 613, 2617
regulator: 14476581915.47603780881857213181004219961152466385778786441
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:54:19 UTC
last updated: 2026-09-26 06:54:19 UTC

(-4100061204731/841, 24018626938158583/24389)
(-4147974505933/841, -94304009082476593/24389)
(17804635907, 2029359747480419)
(-65192469505139/13225, 6175752331839207821/1520875)
(993689520666539/45796, -28417847862697516446433/9800344)
(23661824387, -3361265897899751)
(4507027383059, -9568296462629070007)
(373285565557231/16129, 6632520316360115475581/2048383)
(22740286219373/289, -107778986311066174453/4913)
(26298865996297/256, -134389045719779404621/4096)

2-isogenous partner of curve#1203 (NDElkies); 4-isogenous partner of curve#1374 (jesper-petersen). Isogenous to curve#2090 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:41:24 UTC · history