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curve #3688

y2 + xy = x3 − 24519319585x + 1477772790757961
a-invariants
[1, 0, 0, -24519319585, 1477772790757961]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/5ℤ
conductor (N)
4117912962
discriminant (Δ)
10724981106820835455814863872
Faltings height
4.5616
naive height
83.3818
primes of bad reduction
2, 3, 23, 31, 109, 8831
regulator
9407.526032880879290159710704292337965319481184
submitted by
Michael Rubinstein
submitted at
last updated

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

Commentary

Specialization at t = -1116/23 of the universal curve with a 5-torsion point, y^2 + (t+1)xy + ty = x^3 + tx^2 (as searched in arXiv:2003.00077, Sec. 12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).

last edited by Michael Rubinstein at · history

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