curve #5693

y² + xy = x³ − 33667830492860908865325x + 2416241895394660749602160071570001

a-invariants: [1, 0, 0, -33667830492860908865325, 2416241895394660749602160071570001]
c-invariants: [1616055863657323625535601, -2087632997623410971451752287274784265]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 32486041177166381456220753166751394331525509585798
discriminant (Δ): -79664910409286924089430896671909142906452635996707854668055099998208
Faltings height: 11.8237
naive height: 167.2582
primes of bad reduction: 2, 3, 7, 19, 29, 37, 97, 103, 99680264200468741, 38095706992630278561727
regulator: 346307694067511.709547897623394115491944021396489883187862569660899637092
submitted by: apkorte
submitted at: 2026-10-24 13:05:46 UTC
last updated: 2026-10-24 13:05:46 UTC

Witness: 17 independent points log in to add more points →

(36889311138, -34992283025055297)
(62459886210, -23601384518306529)
(-92197888446, -68823069030431265)
(67535127780, -21225206057756691)
(-135297483582, -67042745959440801)
(73201687818, 18545857229748399)
(130597806840, 15708068513725281)
(85024519746, -12973376535212577)
(242138115906, -91982426784861729)
(-21652504446, 55991826126576735)
(289792553226, 130369536951247023)
(87159556482, -11995935361349601)
(109735699650, -6565714883500449)
(100427284770, -6924390449022561)
(413545845570, -243347139739608609)
(-103392824790, -69224054055846681)
(94453999938, 8880126461665503)

Commentary

Specialization at T = 3/7 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 2026-10-24 13:05:46 UTC · history