Properties

Label 6013.b
Number of curves $1$
Conductor $6013$
CM no
Rank $0$

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

Elliptic curves in class 6013.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6013.b1 6013a1 \([0, -1, 1, -28, 61]\) \(2515456000/294637\) \(294637\) \([]\) \(876\) \(-0.21900\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6013.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 6013.b do not have complex multiplication.

Modular form 6013.2.a.b

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