curve #6256

y² + xy + y = x³ − x² − 1074165304813047x + 14616391394613548743119

a-invariants: [1, -1, 1, -1074165304813047, 14616391394613548743119]
c-invariants: [51559934631026241, -12628561932926400274436961]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 40531433402643104717643452250340307599810
discriminant (Δ): -12970058688845793509645904720108898431939200000
Faltings height: 7.5901
naive height: 115.5960
primes of bad reduction: 2, 5, 4053143340264310471764345225034030759981
regulator: 3149923833184.353219760490552206912179204011086616023532853791540037664
submitted by: The Wren
submitted at: 2026-10-31 23:04:15 UTC
last updated: 2026-10-31 23:04:15 UTC

Witness: 16 independent points log in to add more points →

(4216009983/169, -127090566061018/2197)
(151957383859, -59235663718540818)
(5944152523/169, -313428028238538/2197)
(17906711123/484, -1701119523485957/10648)
(-261954463229/6889, -12529943037771726/571787)
(-1786655953/49, -24978963423266/343)
(-19661034323/841, -4003623464424046/24389)
(124339818183/2209, 37788052188504598/103823)
(7804101104979/14641, 21760728444439072238/1771561)
(-21157693, 166959829886)
(2034777, 111529826586)
(15711427, 40217391486)
(17337627, 34697072286)
(24997277, 58168926136)
(26150067, 66387166046)
(151372843/9, 976149321322/27)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:04:15 UTC · history