curve #6395

y² + xy = x³ − 11548504905176221669965697251x + 474572656889680475241932171102584452105480

a-invariants: [1, 0, 0, -11548504905176221669965697251, 474572656889680475241932171102584452105480]
c-invariants: [554328235448458640158353468049, -410030775552684762101382568520593204149336793]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 11419688444618190533967482030520035564715
discriminant (Δ): 1278141394171205177984272845611043493839640919570054423612950613854522268188659036225
Faltings height: 14.9687
naive height: 205.4627
primes of bad reduction: 3, 5, 7, 11, 19, 31, 37, 89, 137, 167, 191, 283, 509, 929, 1213, 1511, 6779, 63781
regulator: 10478764436.5466909102900764881760955892356752534114868184003
submitted by: The Wren
submitted at: 2026-11-02 01:16:30 UTC
last updated: 2026-11-02 01:16:30 UTC

Witness: 11 independent points log in to add more points →

(-23791445259622008/529, 11561787906554571864789012/12167)
(4587714695548632/529, 7451444008591138463923032/12167)
(36539573202483, 318403306568314280946)
(150493378831475583/1681, 27415038761820619198359711/68921)
(57128975208722757/529, 8490020779187285606633382/12167)
(-19769820963916533/169, 1041410283488492114797527/2197)
(79818538540839, -247612054598344204785)
(85488718404815659887/332929, 729973615970573793556083179418/192100033)
(41820359437727606187/850084, 125161003106405609123975828043/783777448)
(1693023039752180074612/21372129, 23556549440918224664139595854742/98803352367)
(57792914166855, 13433025514429141770)

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=2960/573. 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 [11,11]; torsion Z/2xZ/2 (elltors).

last edited by The Wren at 2026-11-02 01:16:30 UTC · history