Properties

Label 6240.r
Number of curves $1$
Conductor $6240$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 6240.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.r1 6240bb1 \([0, 1, 0, 179, 3419]\) \(153990656/1279395\) \(-5240401920\) \([]\) \(3456\) \(0.54635\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6240.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6240.r do not have complex multiplication.

Modular form 6240.2.a.r

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