curve #333

y² + xy = x³ − 23891105188685143592112789788x + 1419601215093448810627501450420291027410192

a-invariants: [1, 0, 0, -23891105188685143592112789788, 1419601215093448810627501450420291027410192]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 131944541736270829990525135723297231720924027431424328761515243063150
naive height: 207.6435
Faltings height: 15.0848
discriminant (Δ): 2152056942700264818719027733126048402613339655450827996023631575722662975639296000000
primes of bad reduction: 2, 3, 5, 13, 17, 7262584531, 112718068888168147, 4862091821681746797837190485335157793
regulator: 4670728444081471861.943611114955809605351027382415234272937662712114695647415
submitted by: 7fff-zip
submitted at: 2026-08-24 19:17:59 UTC
last updated: 2026-08-24 19:17:59 UTC

Witness: 19 independent points

(802902135464363935216/383161, -22690438940309708009086818304124/237176659)
(56461682270968648/49, -13301264929026283654416068/343)
(657778911301236, -16441039657074125259720)
(6389931597586262770168/48344209, -253987993652797540416741022787452/336137285177)
(79458746926432, -151400256741193904516)
(303353716555143808/5329, -192184625435335240210079492/389017)
(41819388286822169272/9628609, -34273604901646813278927449051300/29877573727)
(-28753310689333592/289, -8238231047207775899063068/4913)
(1296812620898148032452/591361, 46586890441260864333635548737256/454756609)
(1212499903017749954887/401956, 42166051189094922213739956445321/254840104)
(12159610562402775448/3721, 42354737018869119585461129140/226981)
(10408742863846012/121, 41745309263217658764284/1331)
(1629610964813174842297/19571776, -7545777660739706787143667423439/86585537024)
(1621227152774785151669062/36808489, 2064253984470696842385038065304576800/223317102763)
(207286518328532752, -94374891488025371096746076)
(90988414437426738568/9409, -867808711921688565975679471148/912673)
(266709390008921947688965072/3103301501161, 182854778168590565026065125486615701516/5466834887173739659)
(20751533335921432, -2989257151328889938221916)
(1286971669361752, 45850610626306355032324)

Commentary

New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=823/24. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].

last edited by 7fff-zip at 2026-08-24 19:17:59 UTC · history