curve #6422

y² = x³ − 7692021439023008909475x + 255943483084795332664874363411250

a-invariants: [0, 0, 0, -7692021439023008909475, 255943483084795332664874363411250]
c-invariants: [369217029073104427654800, -221135169385263167422451449987320000]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4333929710712664354099132525200
discriminant (Δ): 828327951119249971414856393170815284012659902832626512805264000000
Faltings height: 11.4474
naive height: 162.7970
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 43, 47, 53, 83, 97, 139, 241, 311, 487
regulator: 6186672.587876234440147012314298070952559793770636191364516
submitted by: The Wren
submitted at: 2026-11-02 16:05:07 UTC
last updated: 2026-11-02 16:05:07 UTC

Witness: 10 independent points log in to add more points →

(38483358129, 4113553458311892)
(41676642685, 2784921521006800)
(45563170785, 244651776093900)
(57489279075, 1933331988223350)
(33962802075, 5820310994711850)
(-17504101035, 19627079757516000)
(11051705685, 13125676498552800)
(225742032225/4, 10073495328723225/8)
(-1175935529175/16, -1318269492175711275/64)
(511332664165/9, 41093425513363600/27)

Commentary

Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=2651/1577. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [10,10]; torsion Z/2xZ/2 (elltors).

last edited by The Wren at 2026-11-02 16:05:07 UTC · history