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curve #879

y2 + xy + y = x3 − x2 − 122x + 1721
a-invariants
[1, -1, 1, -122, 1721]
rank (lower bound)
≥ 0
torsion subgroup
ℤ/12ℤ
conductor (N)
90 ☆ record for ℤ/12ℤ torsion, rank ≥ 0
discriminant (Δ)
-1119744000 ☆ record for ℤ/12ℤ torsion, rank ≥ 0
Faltings height
0.4203 ☆ record for ℤ/12ℤ torsion, rank ≥ 0
naive height
28.3891 ☆ record for ℤ/12ℤ torsion, rank ≥ 0
primes of bad reduction
2, 3, 5
regulator
1
submitted by
NDElkies
submitted at
last updated

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Commentary

First curve (LMFDB 90.c7) with a rational point of order 12, the largest allowed by Mazur's theorem. (LMFDB chooses the generator [-9,49].)

last edited by NDElkies at · history

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