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curve #5193

y2 = x3 + 4180x
a-invariants
[0, 0, 0, 4180, 0]
c-invariants
[-200640, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
34944800
discriminant (Δ)
-4674216448000
Faltings height
1.1206
naive height
36.6278
primes of bad reduction
2, 5, 11, 19
regulator
33.455545860939290061649707324867119161116389
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,4,8,13), 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. Selected by height screening in a bounded tuple search, following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.

last edited by The Wren at · history

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