curve #5668

y² = x³ + x² − 23256047562649285076404678633x + 1359511951103422116317243792688687425591963

a-invariants: [0, 1, 0, -23256047562649285076404678633, 1359511951103422116317243792688687425591963]
c-invariants: [1116290283007165683667424574400, -1174618325753363406239796679877127940258902400]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 8822838763774706187970325668285365090230524495813198119194426028805800
discriminant (Δ): 6531001784934224219777621249577355053985288243744766650681318377402442565225890080000
Faltings height: 15.1243
naive height: 207.5627
primes of bad reduction: 2, 3, 5, 11, 17, 37, 109, 1289, 102911, 28150259, 101485648642453093, 4677274257602116832700864911
regulator: 81479129199028784362.862646439894051394648558714128292779230364339084384242185997
submitted by: apkorte
submitted at: 2026-10-24 03:18:07 UTC
last updated: 2026-10-24 03:18:07 UTC

Witness: 21 independent points log in to add more points →

(-128855119884187, -1488861470271095920890)
(-1289266019555581/25, 194522151237055902525078/125)
(82391934558083, -52087955204654692290)
(76423562799629, 168992355895459600194)
(-128857341805042, -1488841654747636464165)
(-347354215460323/4, 13204095482788582828005/8)
(-80365164857707, 1646039133970939878390)
(-145624582508827, -1287623270946788690310)
(104938511552717, 273220415808637146498)
(96287888122763, 113822973112246288110)
(410862688699637/4, -1866831311909069864145/8)
(12964005260006147/169, -360563842104291837329670/2197)
(109846316725493, 361039987231713889110)
(108303508861709, 333410638661994601026)
(-72445767311467, -1632204208599741932790)
(-121408115102077, 1547073909764700272190)
(106812483195227, 306739959122812180878)
(272205559164623, 3898511674533622445310)
(10442907053078, 1057255906573221382935)
(267538409736539, -3779837218526331090546)
(210665421120407, 2410307316777005862318)

Commentary

Specialization at T = -47/19 of the rank-17 fibration of X1152 given in curve#846. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-24 03:18:07 UTC · history