Properties

Label 158a
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 158a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158.c1 158a1 \([1, -1, 1, -9, 9]\) \(72511713/20224\) \(20224\) \([]\) \(32\) \(-0.46658\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 158.2.a.a

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