curve #6277

y² = x³ − 463234874902335172x + 121488874929570091222437700

a-invariants: [0, 0, 0, -463234874902335172, 121488874929570091222437700]
c-invariants: [22235273995312088256, -104966387939148558816186172800]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 28727321523343960013176244938377167208719311048
discriminant (Δ): -14269894784219785321105115205709720530590395692739328
Faltings height: 8.9148
naive height: 133.6469
primes of bad reduction: 2, 19, 43, 231328685847967210052633551330100231984147
regulator: 1212419187242462.53755069457123480688155647891712378676743875219080379063
submitted by: The Wren
submitted at: 2026-10-31 23:38:09 UTC
last updated: 2026-10-31 23:38:09 UTC

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

(346673814, 1600525102594)
(107954313658/9, -35414007407238934/27)
(215135133554/841, 108329424439601606/24389)
(658210730874/1225, -225705835551359318/42875)
(256187933816/625, -10819794544230886/15625)
(1060512780926/5929, -3040433222253829382/456533)
(59216161425/121, 4610039690451785/1331)
(4109950274593/5184, 5931671824120230991/373248)
(105914093344/81, 30508748958777506/729)
(287105466, 3486772758338)
(311732838, 2716013190494)
(379065352, 600574351942)
(387492922, 413519282242)
(403715762, 523297000942)
(413700433, 807730323719)
(846057650, 18308058138130)
(35358007896/169, 12759521050362098/2197)

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 23:38:09 UTC · history