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curve #5084

y2 = x3 + 355832003268x
a-invariants
[0, 0, 0, 355832003268, 0]
c-invariants
[-17079936156864, 0]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
3126331223449826239008
discriminant (Δ)
-2883467035893611830064987878762549248
Faltings height
5.6855
naive height
91.4068
primes of bad reduction
2, 3, 7, 19, 41, 257, 2351
regulator
1115582.2539894042433734991027034960012189421065599
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 (1,6,17,45), 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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