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curve #5001

y2 = x3 − 6921366x
a-invariants
[0, 0, 0, -6921366, 0]
c-invariants
[332225568, 0]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
3065939667581184
discriminant (Δ)
21220490573247709177344
Faltings height
2.9736
naive height
58.8640
primes of bad reduction
2, 3, 43, 139, 193
regulator
3643.79758852206693412479718826405390829083250162
submitted by
The Wren
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,8,9,28), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.

last edited by The Wren at · history

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