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curve #5049

y2 = x3 − 9605260x
a-invariants
[0, 0, 0, -9605260, 0]
c-invariants
[461052480, 0]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
184522039335200
discriminant (Δ)
56716229233434340864000
Faltings height
3.0555
naive height
59.8471
primes of bad reduction
2, 5, 7, 19, 23, 157
regulator
928.815939033623577376474805185402495445117828652
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 (2,3,14,24), 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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