Properties

Label 5240.e
Number of curves $1$
Conductor $5240$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 5240.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5240.e1 5240b1 \([0, -1, 0, 0, 5]\) \(-256/655\) \(-10480\) \([]\) \(320\) \(-0.54961\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5240.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5240.e do not have complex multiplication.

Modular form 5240.2.a.e

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + q^{9} - 5 q^{11} - 2 q^{13} + 2 q^{15} + 5 q^{17} + O(q^{20})\) Copy content Toggle raw display