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curve #5208

y2 = x3 + 13398x
a-invariants
[0, 0, 0, 13398, 0]
c-invariants
[-643104, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
11488409856
discriminant (Δ)
-153921715250688
Faltings height
1.4118
naive height
40.1222
primes of bad reduction
2, 3, 7, 11, 29
regulator
103.0761310278705121743825142108443322498445761
submitted by
The Wren
submitted at
last updated

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Commentary

Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (5,14,18,21), 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 in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at · history

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