Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 6240.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.k1 6240x1 \([0, -1, 0, -93965, 11254725]\) \(-22400965661211136/321826171875\) \(-1318200000000000\) \([]\) \(29568\) \(1.7062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6240.k1 has rank \(1\).

Complex multiplication

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

Modular form 6240.2.a.k

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