Properties

Label 13520.a
Number of curves $1$
Conductor $13520$
CM no
Rank $1$

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

Elliptic curves in class 13520.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13520.a1 13520f1 \([0, 1, 0, -56, 820]\) \(-338/5\) \(-292464640\) \([]\) \(5760\) \(0.30592\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13520.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 13520.a do not have complex multiplication.

Modular form 13520.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} - 3 q^{7} + q^{9} + 5 q^{11} + 2 q^{15} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display