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curve #5209

y2 = x3 − 14637x
a-invariants
[0, 0, 0, -14637, 0]
c-invariants
[702576, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
6855736608
discriminant (Δ)
200694833462592
Faltings height
1.4339
naive height
40.3875
primes of bad reduction
2, 3, 7, 17, 41
regulator
65.04883192446198650465198160757752600804799882
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 (4,6,15,16), 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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