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curve #5210

y2 = x3 − 21177x
a-invariants
[0, 0, 0, -21177, 0]
c-invariants
[1016496, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1594543392
discriminant (Δ)
607817617422912
Faltings height
1.5262
naive height
41.4956
primes of bad reduction
2, 3, 13, 181
regulator
55.22018662897916614699147957419890793848916546
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 (1,6,10,15), 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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