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curve #5076

y2 = x3 − 32502332577x
a-invariants
[0, 0, 0, -32502332577, 0]
c-invariants
[1560111963696, 0]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
33804851934269294749728
discriminant (Δ)
2197473080567724722869798872578112
Faltings height
5.0872
naive height
84.2273
primes of bad reduction
2, 3, 11, 13, 19, 37, 47, 2293
regulator
743056.46334424658521923848644224393220714350957064
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 (3,4,31,60), 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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