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curve #5203

y2 = x3 + 12483x
a-invariants
[0, 0, 0, 12483, 0]
c-invariants
[-599184, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
554045472
discriminant (Δ)
-124490693285568
Faltings height
1.3941
naive height
39.9100
primes of bad reduction
2, 3, 19, 73
regulator
100.7029554965005419957921527815216782955889979
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,3,6,10), 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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