Properties

Label 58.a
Number of curves $1$
Conductor $58$
CM no
Rank $1$

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

Elliptic curves in class 58.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58.a1 58a1 \([1, -1, 0, -1, 1]\) \(-185193/116\) \(-116\) \([]\) \(4\) \(-0.90223\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 58.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 58.a do not have complex multiplication.

Modular form 58.2.a.a

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