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curve #5197

y2 = x3 − 5037x
a-invariants
[0, 0, 0, -5037, 0]
c-invariants
[241776, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
811883808
discriminant (Δ)
8178917481792
Faltings height
1.1672
naive height
37.1873
primes of bad reduction
2, 3, 23, 73
regulator
64.00045205127535212964565537438378414468288753
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,12,20,21), 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 by height screening 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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