Properties

Label 1913.a
Number of curves $1$
Conductor $1913$
CM no
Rank $2$

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

Elliptic curves in class 1913.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1913.a1 1913a1 \([1, 1, 0, -202, 1025]\) \(-918613512361/1913\) \(-1913\) \([]\) \(300\) \(-0.12104\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1913.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 1913.a do not have complex multiplication.

Modular form 1913.2.a.a

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