Properties

Label 4013.a
Number of curves 1
Conductor 4013
CM no
Rank 0

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Show commands for: SageMath
sage: E = EllipticCurve("4013.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4013.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4013.a1 4013a1 [0, 1, 1, -6, 3] [] 430 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4013.a1 has rank \(0\).

Modular form 4013.2.a.a

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