curve #6249

y² = x³ + x² − 2176181004084740x + 38634864427450373637984

a-invariants: [0, 1, 0, -2176181004084740, 38634864427450373637984]
c-invariants: [104456688196067536, -33380523492057251999623360]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 2900836471454746643444186032359612504
discriminant (Δ): 14750253028246023080660732131127815161367709952
Faltings height: 7.6672
naive height: 117.5626
primes of bad reduction: 2, 3, 13, 23, 1979, 23761, 8382529, 1025546233472101729
regulator: 82535756126.714375892067858043137061702070834893621350226593435461099
submitted by: The Wren
submitted at: 2026-10-31 22:45:58 UTC
last updated: 2026-10-31 22:45:58 UTC

Witness: 15 independent points log in to add more points →

(95389144, -836065261512)
(-11292200279/256, 904846690877931/4096)
(6006181438/121, -306180601257330/1331)
(29707596241/784, -2258093405000511/21952)
(896169346/25, -10222972115694/125)
(3575322136/121, -15234908231016/1331)
(288474214/9, 1149496610678/27)
(137835633646/1849, 42865256373910686/79507)
(5075789926/49, 329841082639074/343)
(-53406074, 50307852114)
(-46033670, 203131905678)
(-27716033, 278673840666)
(-12474209, 252665670114)
(37848940, 102415465728)
(1183641478, 40690944816210)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 15 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_15.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 22:45:58 UTC · history