curve #6260

y² = x³ + x² − 112113119041269810x + 11334433576197272916992409

a-invariants: [0, 1, 0, -112113119041269810, 11334433576197272916992409]
c-invariants: [5381429713980950896, -9792950642123022084167146720]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 42638728013663757881245066031834182468289480508
discriminant (Δ): 34689334117708341516897260901123144825631462920010512
Faltings height: 8.7947
naive height: 129.3885
primes of bad reduction: 2, 3, 31, 563, 15920806019323, 12787565016588072544063606811
regulator: 35603945556192113.2899591982582192749535714373617863134197172642108455829
submitted by: The Wren
submitted at: 2026-10-31 23:17:19 UTC
last updated: 2026-10-31 23:17:19 UTC

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

(3403314606, -197607795558651)
(-117383406, 4783016137617)
(396391644, -5401601297817)
(17198483934/49, -1338296518127043/343)
(305997873, -2383291048245)
(-76230519306/1369, -211318432572938553/50653)
(-1179724146/121, -4691956377501297/1331)
(49174391712/169, 4019860168713225/2197)
(1021052224776/3481, 394300838472124329/205379)
(-163619484, 5029712932401)
(14022642, 3124911003471)
(475776804, 8105069209743)
(13993017681, 1654792729460901)
(-22364283/4, 27667848407295/8)
(270706180737/3721, 428456286198035091/226981)
(9653060958726/97969, 34205806701293409621/30664297)
(32741091422877/13924, 185517369251993439405/1643032)

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 23:17:19 UTC · history