curve #5228

y² = x³ + 8769348x

a-invariants: [0, 0, 0, 8769348, 0]
c-invariants: [-420928704, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 17089214298912
discriminant (Δ): -43160044963315780620288
Faltings height: 3.0327
naive height: 59.5739
primes of bad reduction: 2, 3, 7, 17, 23, 89
regulator: 429.433510772698785864760387036528665866826454847
submitted by: The Wren
submitted at: 2026-10-21 10:37:28 UTC
last updated: 2026-10-21 10:37:28 UTC

Witness: 5 independent points log in to add more points →

(714, 81396)
(1173, 109089)
(1428, 124236)
(2346, 182988)
(4692, 380052)

Commentary

Rational 2-isogeny partner of curve #5227: https://elliptic-rank.icarm.cloud/curve/5227. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,7,15,19), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.

last edited by The Wren at 2026-10-21 10:37:28 UTC · history