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curve #3385

y2 + xy = x3 − 278232714x + 1786218031908
a-invariants
[1, 0, 0, -278232714, 1786218031908]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/8ℤ
conductor (N)
3542322
discriminant (Δ)
128831394594552830836992
Faltings height
3.5012
naive height
69.9455
primes of bad reduction
2, 3, 7, 19, 23, 193
regulator
6.37106246009307405102742021086654808275427
submitted by
David Renshaw
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/8ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=(2t-1)(t-1), c=b/t, at t = 2/23; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 3542322, torsion ℤ/8ℤ.

last edited by David Renshaw at · history

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