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curve #1083

y2 = x3 + x2 − 25x + 39
a-invariants
[0, 1, 0, -25, 39]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ
conductor (N)
1088 ☆ record for ℤ/2ℤ torsion, rank ≥ 2
discriminant (Δ)
69632
Faltings height
-0.3032
naive height
21.3100
primes of bad reduction
2, 17
regulator
0.531665631644888496256262446826464461629107
submitted by
NDElkies
submitted at
last updated

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Commentary

This is LMFDB curve 1088.a2; together with the 2-isogenous 1088.a1 it is has the smallest conductor for torsion Z/2Z.

last edited by NDElkies at · history

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