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curve #5071

y2 = x3 + 1118207475x
a-invariants
[0, 0, 0, 1118207475, 0]
c-invariants
[-53673958800, 0]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
177832953905191200
discriminant (Δ)
-89484362261151858514899000000
Faltings height
4.2448
naive height
74.1186
primes of bad reduction
2, 3, 5, 7, 11, 19, 43, 79
regulator
3715.8930157299186761226525629522604644410599723926
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (10,18,36,60), 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 using a small-prime sieve and height screening, following the search approach 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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