curve #2091

y² = x³ − 84328417414643930463747x − 3938366605811751978165202514751614

a-invariants: [0, 0, 0, -84328417414643930463747, -3938366605811751978165202514751614]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 81988082219777126188462072560
discriminant (Δ): 31679085932749793358568834548575981499312020110637728162686000000000000
Faltings height: 12.2217
naive height: 169.9806
primes of bad reduction: 2, 3, 5, 7, 11, 31, 41, 89, 107, 109, 127, 131, 137, 163, 337, 1279
regulator: 35628697642.57981255965173108151241631110098387752269159035
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:55:10 UTC
last updated: 2026-09-26 06:55:10 UTC

(-229660402593, -57579043584503650)
(-491335408647/4, -540617810859876875/8)
(-5931677762353/121, 11738754602704946250/1331)
(-4825103885233777/100489, 7969579987914151155450/31855013)
(-24557881927698/361, 264179465546670700600/6859)
(-7427793077241822/49729, 809237254052456503463750/11089567)
(-255949859193, -29633091477508750)
(-67128279741697/529, 835832830839098467950/12167)
(1760582467407, -2303211897512621150)
(23284549315535319/9025, -3530065473387776627212622/857375)

2-isogenous partner of curve#1085 (dujella); 4-isogenous partner of curve#1137 (David Renshaw). Isogenous to curve#2023 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:41:36 UTC · history