Properties

Label 258.b
Number of curves $1$
Conductor $258$
CM no
Rank $1$

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

Elliptic curves in class 258.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
258.b1 258a1 \([1, 1, 0, 3, -3]\) \(1685159/8256\) \(-8256\) \([]\) \(24\) \(-0.56617\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 258.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 258.b do not have complex multiplication.

Modular form 258.2.a.b

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