curve #3527

y² + xy + y = x³ + x² + 356255228079292143418234698872137x + 1070554682824230207930568348551030335484270850781

a-invariants: [1, 1, 1, 356255228079292143418234698872137, 1070554682824230207930568348551030335484270850781]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 11295873917088249179522235693451896437885004482470852950
discriminant (Δ): -3388877748183820404831840304393824528555316514461605170967300689148539257492031084475751531787250000
Faltings height: 17.7867
naive height: 236.4732
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 29, 43, 53, 61, 71, 83, 97, 109, 167, 241, 277, 421, 449, 3533, 5563, 14923, 16267, 838003
regulator: 20051405226707667.95549026804039593966431721793849287399551070139242295
submitted by: wgxli
submitted at: 2026-09-27 20:21:41 UTC
last updated: 2026-09-27 20:21:41 UTC

(417208047327675, 1104201001049794294620262)
(-1692847849644675, 680159934004328122531162)
(-1734531192881455, 668879937193265430949852)
(-2066207800744575, 570645483661722069619762)
(1396125951725745, 1253257010356077959541052)
(4128402276942309, 1616070185030475399658288)
(7758696176486235, 2074050100380563919954382)
(13458436782441345, 2881477626558187464138802)
(16806235401366651, 3435808121825284266356038)
(16971407361168129, 3464817322391884511781682)
(24885547350985925, 5034634360550888477038762)
(37936729919376045, 8317696967821191593811352)
(184511997276752385, 79677194222839496272255282)
(388978932103432885, 242886705504482428491571082)
(404246030092235675, 257303110616938233853654262)
(69977956033503680121/7921, 1561693490564736066112102009172/704969)

Construction adapted from S. Kihara, Proc. Japan Acad., 77, Ser. A (2001). Parameters (a, b, c, u) = (63, 190, 587, 186).

last edited by wgxli at 2026-09-27 20:21:42 UTC · history