Properties

Label 71058b
Number of curves $1$
Conductor $71058$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 71058b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71058.b1 71058b1 \([1, 1, 0, -32, 48]\) \(3803721481/568464\) \(568464\) \([]\) \(8960\) \(-0.17143\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 71058b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 71058b do not have complex multiplication.

Modular form 71058.2.a.b

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