curve #5568

y² = x³ − 9744941714813720895282487x + 11136093681707102462377130172062517466

a-invariants: [0, 0, 0, -9744941714813720895282487, 11136093681707102462377130172062517466]
c-invariants: [467757202311058602973559376, -9621584940994936527493840468662015090624]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 404620717008459394169120759517306168913862046883774222840479160
discriminant (Δ): 5653288433244208645329096063920227952913329394684724687828397797989940000000
Faltings height: 13.2909
naive height: 184.2300
primes of bad reduction: 2, 5, 7, 13, 23, 79, 8863, 976837185197, 7066247935256487713449518673895650842787
regulator: 6637889266789083319.80875533012643427520331470818523101089800418364635718738790
submitted by: apkorte
submitted at: 2026-10-23 11:25:55 UTC
last updated: 2026-10-23 11:25:55 UTC

Witness: 20 independent points log in to add more points →

(1453173693677, -209015919969288250)
(-423282140823, -3896808303648464750)
(573478357677, -2395033318764544250)
(2128098118527, -188774261543611900)
(-1725755377823, -4776377289426720250)
(-6082892123, 3345948428446953550)
(-4921787127767/9, -109013539540493608930/27)
(2170994653377, -460703736466286950)
(1466179364927, 8972968031345500)
(-3002483466615, 3650754845395980686)
(7637016135077, 19548280323464918350)
(9205959672927, 26488239161748071500)
(2272571292177, -852581827551522250)
(1124946213902, 1263796783745089100)
(318470616067837/81, 4225715965148316798250/729)
(1447340303777, 252441080231854150)
(-1663157123534807/2209, -441049541933215026143150/103823)
(2416929353297, 1304555718857215370)
(2135503589587, 253838714134509140)
(3197816612722, -3560130513535629670)

Commentary

Specialization at T = -8/7 of the rank-17 fibration of X1152 given in curve#3897. 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 2026-10-23 11:25:55 UTC · history