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curve #3400

y2 + xy = x3 − 125268546914x + 17065181337340500
a-invariants
[1, 0, 0, -125268546914, 17065181337340500]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/8ℤ
conductor (N)
16824234
discriminant (Δ)
2617227016901882338755312
Faltings height
4.7036
naive height
88.2748
primes of bad reduction
2, 3, 7, 19, 29, 727
regulator
40.1069051925038460665734191783063743132247
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 = 1/58; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 16824234, torsion ℤ/8ℤ.

last edited by David Renshaw at · history

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