curve #5072

y² = x³ − 4472829900x

a-invariants: [0, 0, 0, -4472829900, 0]
c-invariants: [214695835200, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 177832953905191200
discriminant (Δ): 5726999184713718944953536000000
Faltings height: 4.5914
naive height: 78.2775
primes of bad reduction: 2, 3, 5, 7, 11, 19, 43, 79
regulator: 3715.8930157299186761226525629522604644410599723926
submitted by: The Wren
submitted at: 2026-10-21 02:06:14 UTC
last updated: 2026-10-21 02:06:14 UTC

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

(-59850, 7301700)
(-56880, 8389800)
(67725, 2776725)
(105070, 26267500)
(109494, 28687428)
(304150, 163632700)

Commentary

Rational 2-isogeny partner of curve #5071: https://elliptic-rank.icarm.cloud/curve/5071. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (10,18,36,60), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.

last edited by The Wren at 2026-10-21 02:06:15 UTC · history