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curve #3358

y2 + xy = x3 − 1111313922400x + 450918714629292032
a-invariants
[1, 0, 0, -1111313922400, 450918714629292032]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/10ℤ
conductor (N)
168077130
discriminant (Δ)
1980809600967795936308490000000000
Faltings height
5.5335
naive height
94.8233
primes of bad reduction
2, 3, 5, 13, 17, 101, 251
regulator
14.3675842136920189358005985088525832565765
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/10ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with d=t^2/(t-(t-1)^2), c=td-t, b=cd, at t = 15/17; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 168077130, torsion ℤ/10ℤ.

last edited by David Renshaw at · history

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