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curve #5350

y2 = x3 − 1029526722392x
a-invariants
[0, 0, 0, -1029526722392, 0]
c-invariants
[49417282674816, 0]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
4239701088476856936806656
discriminant (Δ)
69838169048661973147143129899037458432
Faltings height
5.9511
naive height
94.5940
primes of bad reduction
2, 7, 19, 31, 109, 233, 1229
regulator
987124779.419637045747458003598609557742373179472540356
submitted by
The Wren
submitted at
last updated

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Commentary

Rational 2-isogeny partner of curve #5349: https://elliptic-rank.icarm.cloud/curve/5349. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,8,16,30), 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. Eight rational points transported through the isogeny and checked exactly. Rank ≥8 follows from the source curve through the rational isogeny. Rational torsion C2.

last edited by The Wren at · history

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