curve #1100

y² + xy = x³ + 88871190402766374892305201263009054x + 3984685924354438849515723880588291198007040526340420

a-invariants: [1, 0, 0, 88871190402766374892305201263009054, 3984685924354438849515723880588291198007040526340420]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 2560824921463903740108076133817775448204077218700778327571510
discriminant (Δ): -51781577496040709634338662315247451369154842684564648521344349362540092926308890113955511886507530644983040
Faltings height: 19.1653
naive height: 253.0311
primes of bad reduction: 2, 3, 5, 11, 17, 23, 29, 47, 53, 67, 73, 137, 193, 263, 311, 613, 647, 1091, 21589, 276047, 25155547
regulator: 97194451660008298.46095422680816229636464890000525914903509510037975912
submitted by: dujella
submitted at: 2026-09-23 19:24:17 UTC
last updated: 2026-09-23 19:24:17 UTC

(151973772990544676, 144916412062834947325089374)
(2483151276492131324/25, 14679826610543776415004288958/125)
(1610418222555057704, 2079336080580622560199851146)
(4634585828316182444/25, 20475216698846556208892216662/125)
(-43256174748154756, -7715030657930259201193330)
(72902402348883620, 104168459661214206318188990)
(452835459272043074, 370252792228077611247142466)
(153321526455960346904/25, 1900732161197395082302431092182/125)
(2134230041464174184/25, 13803142047956961346950385942/125)
(82891046930330024, 109182645833355896465324810)
(375401087875922171036/1681, 12888190018226387298012343424614/68921)
(196347242398027736, 170305387431896979433767194)
(271776890222171386, 219572290075495322173230370)
(234450949350981596/25, 8677330466865166648614606166/125)
(11767892998547671020716/289, 1276614337651341056305878640548910/4913)
(37857943848339470264/289, 656844213086979152886012631450/4913)

found by Dujella (2009)

last edited by dujella at 2026-09-23 19:24:17 UTC · history