curve #6267

y² + xy = x³ − x² − 175794244176026716639x + 924139424489542810017330367009

a-invariants: [1, -1, 0, -175794244176026716639, 924139424489542810017330367009]
c-invariants: [8438123720449282398681, -798456462720993431112951666301725]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 795674228819300344739553923797214936788267268052782
discriminant (Δ): -21251164451029323090294950562147074296848045520718025039649028
Faltings height: 10.5400
naive height: 151.5205
primes of bad reduction: 2, 7, 19, 31, 71, 425811887, 167981800022770708746362587734947359
regulator: 152686520701706326.11916240557590408344504518295497096377255842563931966858
submitted by: The Wren
submitted at: 2026-10-31 23:27:54 UTC
last updated: 2026-10-31 23:27:54 UTC

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

(1084296139136, 1128988049709794799)
(1718273689812, -2252297661457811437)
(1695371666989/9, 2202158722087378138/27)
(16940901090960/289, -68084728724874009169/4913)
(4783732418605/144, -9736191350229775361/1728)
(69289682205414/4489, 413283019807066511077/300763)
(46291924693174/7569, 183617934300521489257/658503)
(1898838730537/576, -8526673033363930025/13824)
(28270341257004/9409, -593639898628534672103/912673)
(-3468073700, 1221514910738297)
(-727047972, 1025459263994795)
(5878674200, 306366647115697)
(8123367343, 179305385056427)
(28115475136, 4266872380988049)
(-17700175556/25, 127980027937041343/125)
(549328287809/64, 111703513763142693/512)
(596004090640/169, 1296107556717154251/2197)
(220758139722470/22201, 1320217993764635493087/3307949)

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 23:27:55 UTC · history