Properties

Label 457056.k
Number of curves $1$
Conductor $457056$
CM no
Rank $1$

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

Elliptic curves in class 457056.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457056.k1 457056k1 \([0, 0, 0, 114264, -5256144]\) \(1536\) \(-107413969423085568\) \([]\) \(3421440\) \(1.9568\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457056.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 457056.k do not have complex multiplication.

Modular form 457056.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{7} - 2 q^{11} + q^{13} - 6 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display