Properties

Label 9600.by
Number of curves $2$
Conductor $9600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 9600.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9600.by1 9600bv1 \([0, 1, 0, -7658, 247938]\) \(24836849888/820125\) \(1640250000000\) \([2]\) \(18432\) \(1.1170\) \(\Gamma_0(N)\)-optimal
9600.by2 9600bv2 \([0, 1, 0, 2467, 865563]\) \(6483584/1265625\) \(-324000000000000\) \([2]\) \(36864\) \(1.4636\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9600.by have rank \(1\).

Complex multiplication

The elliptic curves in class 9600.by do not have complex multiplication.

Modular form 9600.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{7} + q^{9} + 2 q^{11} - 6 q^{13} + 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.