Properties

Label 53550cd
Number of curves $1$
Conductor $53550$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 53550cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53550.t1 53550cd1 \([1, -1, 0, -10242, 1176916]\) \(-417267265/1850688\) \(-527012325000000\) \([]\) \(172800\) \(1.5097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53550cd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53550cd do not have complex multiplication.

Modular form 53550.2.a.cd

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 2 q^{11} + q^{14} + q^{16} - q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display