Properties

Label 6440k
Number of curves $1$
Conductor $6440$
CM no
Rank $1$

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

Elliptic curves in class 6440k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6440.g1 6440k1 \([0, -1, 0, -180, 1897]\) \(-40535147776/67648175\) \(-1082370800\) \([]\) \(1920\) \(0.42434\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6440k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6440k do not have complex multiplication.

Modular form 6440.2.a.k

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