curve #5302

y² = x³ + 101704948x

a-invariants: [0, 0, 0, 101704948, 0]
c-invariants: [-4881837504, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 20687792895365408
discriminant (Δ): -67329628821053064372441088
Faltings height: 3.6454
naive height: 66.9264
primes of bad reduction: 2, 17, 19, 223, 353
regulator: 17029.818929277147392034590510657859401192751087340
submitted by: The Wren
submitted at: 2026-10-21 12:45:05 UTC
last updated: 2026-10-21 12:45:05 UTC

Witness: 6 independent points log in to add more points →

(68, 83164)
(446, 213188)
(1412, 382652)
(157438/9, 72106604/27)
(207613/9, 103242979/27)
(2676446/121, 4812249908/1331)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (4,11,13,20), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3.

last edited by The Wren at 2026-10-21 12:45:05 UTC · history