curve #1803

y² = x³ + x² − 3383044565362668792508854542324233x + 75737263950801942103904570668638566598532431572663

a-invariants: [0, 1, 0, -3383044565362668792508854542324233, 75737263950801942103904570668638566598532431572663]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 207871256848409744593342350561253204800
discriminant (Δ): 911981998986183047761413416183206545752553412386768512865668602893397070733232542617096256000000
Faltings height: 17.7983
naive height: 243.2259
primes of bad reduction: 2, 3, 5, 13, 17, 23, 37, 41, 101, 359, 389, 541, 12479, 23209, 49411, 51431
regulator: 348545797296.277062008862168967922814386554169478065932579861
submitted by: hdeping
submitted at: 2026-09-25 15:05:28 UTC
last updated: 2026-09-25 15:05:28 UTC

Witness: 11 independent points log in to add more points →

(21966937543749263, 3467304529380020399592600)
(33560959657313363, 5137371389991712861800)
(34582038915915083, 319292566508771961823200)
(134483428957332077/4, 96800241541200000930525/8)
(31780818196317203, 566228347995386167907400)
(1413627031281777887/49, 502860429284713027048333800/343)
(9700355475181684787/289, 16274604587975225427493800/4913)
(33623189883813803, 12873137085655241194800)
(33548281734503453, 9678428398238096687400)
(173923494287946441475667/2809, 72533258254815185975583870670539600/148877)
(-2251179780875766539120038/34421689, 839055527133163935536879014270829625/201952049363)

Commentary

Rank 11 with torsion Z/2Z x Z/2Z induced by a rational Diophantine triple, smallest known conductor in its class (Dujella-Peral 2017/2020); witness points from the paper.

last edited by hdeping at 2026-09-27 08:23:52 UTC · history