curve #6263

← home · all curves · JSON ↓

y² = x³ − 108666925090406767x + 29180065293583726182199570

a-invariants

[0, 0, 0, -108666925090406767, 29180065293583726182199570]

c-invariants

[5216012404339524816, -25211576413656339421420428480]

rank (lower bound)

≥ 17

torsion subgroup

trivial

conductor (N)

10616577812283025896558154870543298193305276283064

discriminant (Δ)

-285713342084160792928173063876061240978231595329818368

Faltings height

8.9466

naive height

130.7942

primes of bad reduction

2, 29, 73536722285566771631401, 622289243218313411599627

regulator

687740217914250.636999407102393980283414416574421441837629514145509974938

submitted by

The Wren

submitted at

2026-10-31 23:21:58 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-31 23:29:45 UTC

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

(637842721/4, 31906546738777/8)
(319882179243, -180919274973240064)
(-330970014303/1681, 451645220707895398/68921)
(5273678169/16, -345665098998179/64)
(13158072085/81, -2899030245005690/729)
(5466866361/361, -35993690939323982/6859)
(516766534861/841, 340059706461990098/24389)
(547917209109/289, 400279241918204486/4913)
(20698818642261/10609, 93004886460745007558/1092727)
(-369985715, 4328757546110)
(-283513859, 6099161409262)
(-197005507, 6553017151186)
(-165213322, 6528684275536)
(323812953, 5286365391214)
(619732761, 14137028138158)
(1359374417, 48922871838038)
(59876979931, 14651540125001272)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:21:58 UTC · history