Properties

Label 158.a
Number of curves $1$
Conductor $158$
CM no
Rank $1$

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

Elliptic curves in class 158.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158.a1 158b1 \([1, 1, 0, -3, 1]\) \(4826809/316\) \(316\) \([]\) \(8\) \(-0.77057\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 158.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 158.a do not have complex multiplication.

Modular form 158.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} - 2 q^{9} + q^{10} + 4 q^{11} - q^{12} - 7 q^{13} + 3 q^{14} + q^{15} + q^{16} - 4 q^{17} + 2 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display