Properties

Label 131a
Number of curves $1$
Conductor $131$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 131a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
131.a1 131a1 \([0, -1, 1, 1, 0]\) \(32768/131\) \(-131\) \([]\) \(2\) \(-0.91105\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 131a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 131a do not have complex multiplication.

Modular form 131.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - 2 q^{5} - q^{7} - 2 q^{9} + 2 q^{12} - 3 q^{13} + 2 q^{15} + 4 q^{16} + 4 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display