curve #6264

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y² + xy = x³ − x² − 253909844844956916x + 49143623687742991412814956

a-invariants

[1, -1, 0, -253909844844956916, 49143623687742991412814956]

c-invariants

[12187672552557931977, -42460090811365418094161428101]

rank (lower bound)

≥ 17

torsion subgroup

trivial

conductor (N)

8951284333576991526866634801648665835908400258

discriminant (Δ)

4334372997435983683156308170384713673731893756128244

Faltings height

8.7875

naive height

131.8409

primes of bad reduction

2, 3, 7, 61, 4649, 12487, 33507307, 598725547402888103823693983

regulator

912503980769535.189338263746608114390890391175051741052418712943473762842

submitted by

The Wren

submitted at

2026-10-31 23:23:59 UTC

later contributions

primes of bad reduction recorded · Maksym Voznyy · 2026-10-31 23:27:14 UTC

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

(344112232261/400, -172956830424615769/8000)
(33128482051/4, -6018915588082075/8)
(976655771/100, 6831153885503101/1000)
(11767188986/121, 6704100885937140/1331)
(217699153903/1369, 181132513781265823/50653)
(229227648391/1156, -100915503042104765/39304)
(36584230717/121, 154132876637981/1331)
(7043118086431/10201, 14677908579289946879/1030301)
(18361366604/25, 2011019469881982/125)
(105590380, 4848704622286)
(145438846, 3910382231140)
(1217389831/4, 1920680891003/8)
(309170926, 441091841134)
(312858742, 572999739172)
(3469078774, 202277688597796)
(5827077439, 443197970635195)
(62427462031/25, 15301889020861814/125)

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 23:23:59 UTC · history