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curve #5182

y2 = x3 − 8422225x
a-invariants
[0, 0, 0, -8422225, 0]
c-invariants
[404266800, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
90795358656800
discriminant (Δ)
38234946978163369000000
Faltings height
3.0226
naive height
59.4528
primes of bad reduction
2, 5, 7, 17, 19, 149
regulator
395.1713816261585978395753634062242054643458717
submitted by
The Wren
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (2,5,10,13), followed by a rational 2-isogeny and 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 by height screening in a bounded tuple search, following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at · history

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