curve #5241

y² = x³ + 20794959108x

a-invariants: [0, 0, 0, 20794959108, 0]
c-invariants: [-998158037184, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 96095627622976034592
discriminant (Δ): -575511738300685981614134437613568
Faltings height: 4.9755
naive height: 82.8875
primes of bad reduction: 2, 3, 7, 11, 19, 67, 71, 83
regulator: 34991.86022742262041584364940380427888439445127371234
submitted by: The Wren
submitted at: 2026-10-21 10:55:15 UTC
last updated: 2026-10-21 10:55:15 UTC

Witness: 7 independent points log in to add more points →

(14058, 17178876)
(38346, 29219652)
(121429, 65693089)
(126522, 68237532)
(194469, 106763481)
(227088, 128191176)
(777876, 697754772)

Commentary

Rational 2-isogeny partner of curve #5240: https://elliptic-rank.icarm.cloud/curve/5240. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,15,16,18), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.

last edited by The Wren at 2026-10-21 10:55:15 UTC · history