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curve #5235

y2 = x3 − 188116701x
a-invariants
[0, 0, 0, -188116701, 0]
c-invariants
[9029601648, 0]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1132412582243948832
discriminant (Δ)
426051438285245662977286464
Faltings height
3.7992
naive height
68.7713
primes of bad reduction
2, 3, 19, 23, 43, 47, 71
regulator
15081.306864827138322561402483971274886624357712509
submitted by
The Wren
submitted at
last updated

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

Commentary

Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (4,7,11,13), 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 in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.

last edited by The Wren at · history

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