curve #1198

y² + xy = x³ − 1573649343823368540876031311163x + 759700447776441994545662848372757124914524817

a-invariants: [1, 0, 0, -1573649343823368540876031311163, 759700447776441994545662848372757124914524817]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 688038028320098121783655338615679833504856167124350
discriminant (Δ): 77720186439626222031133330446093684661526443521956063658751926056122140280976813136000000
Faltings height: 16.0603
naive height: 220.2065
primes of bad reduction: 2, 3, 5, 23, 31, 41, 67, 71, 79, 137, 197, 257, 337, 379, 439, 1063, 1129, 1993, 2089, 2671
regulator: 4723229906290542.7190945761010286626062883981155479769510772823919413
submitted by: dujella
submitted at: 2026-09-23 22:25:30 UTC
last updated: 2026-09-23 22:25:30 UTC

(736514034219422, 458051495820921115889)
(762611160455882, 1770332236107660810509)
(241155905932406, 19855233918376765321505)
(194771754151600022, 85956748191903474189783689)
(612475617028382, 5063037998649968258609)
(681223001784722, 1955995370438330716889)
(713586963578522, 357500952850315853789)
(731750663034422, 63240180691528105889)
(-1090062926727778, -34348564992167678404111)
(198536812179296486/121, 67803436219902817183508299/1331)
(18330212232534656/25, 29680366770573301551739/125)
(731632950881882, 13316104610295872009)
(-529228154016012418/529, -444176165192718284305398761/12167)
(229711193000672, 20256771678786941459639)
(241584278923634357/16, 118344255883242245864080061/64)

found by Dujella (2009)

last edited by dujella at 2026-09-23 22:25:30 UTC · history