curve #6423

y² = x³ − 44825825608844171687676x + 3252076392547469789257538724103440

a-invariants: [0, 0, 0, -44825825608844171687676, 3252076392547469789257538724103440]
c-invariants: [2151639629224520241008448, -2809794003161013897918513457625372160]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5763174267608696604990665002229568
discriminant (Δ): 1195710394997773314358395846806197782372683163118199542934795044798464
Faltings height: 11.9856
naive height: 168.0848
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 23, 31, 41, 47, 79, 109, 199, 239, 317, 337, 587, 877
regulator: 69649204.74332628648093086353912299048473447274353491155066
submitted by: The Wren
submitted at: 2026-11-02 16:05:42 UTC
last updated: 2026-11-02 16:05:42 UTC

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

(313382641632, -141355354845155724)
(6577188726798/169, 86954567664778905168/2197)
(7980768303229/9, -21947889206253885875/27)
(2516280408006, 3977776713509533440)
(5432848970577/64, 3919263908220474201/512)
(12835874000406/25, -42497485704478262304/125)
(156795287904, -8852855186286540)
(-11717095113090/49, -5918898579193584720/343)
(602618851804, -441678516383784680)
(191290498927065/16, -2645284604194258481565/64)

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=3476/2219. 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 16:05:42 UTC · history