curve #6266

y² = x³ − 170364434238838852687x + 811783598798924467766606521810

a-invariants: [0, 0, 0, -170364434238838852687, 811783598798924467766606521810]
c-invariants: [8177492843464264928976, -701381029362270740150348034843840]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 11263947205505276370500249815376820412893317391816209656
discriminant (Δ): 31773702723599859754750960687209027078942682284991702316353792
Faltings height: 10.5549
naive height: 151.3670
primes of bad reduction: 2, 7, 257, 272110933, 620856747239, 4632677404619479303670913721139
regulator: 137731480853551159.69095932309382511634141121225614553538655681286432016698
submitted by: The Wren
submitted at: 2026-10-31 23:26:36 UTC
last updated: 2026-10-31 23:26:36 UTC

Witness: 18 independent points log in to add more points →

(23210033101, -3059574332630582)
(-11897904495, 1074474031027250)
(278455081273/16, -113010434425226989/64)
(1391756770717/121, -813923822298045578/1331)
(12277062089071/1369, -3652723704515219152/50653)
(8733084990937/841, 9829259832144645382/24389)
(36801183951355/3481, 90061895272441627640/205379)
(12957453973, 883059435837026)
(66446041387459/5041, 331198969256623656104/357911)
(-8510633531, 1282676951901646)
(-2370317167, 1096487092363726)
(3473035313, 511853069977774)
(6075947443, 31061815320424)
(9975816913, 324070669381774)
(11654468342, 639737352281888)
(18167001257, 1926813072375562)
(18446529877, 1986462697477538)
(52180062945/4, 7196794722093305/8)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 18 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_18.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:26:37 UTC · history