Properties

Label 5880.x
Number of curves $2$
Conductor $5880$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 5880.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5880.x1 5880j1 \([0, 1, 0, -51, 90]\) \(2725888/675\) \(3704400\) \([2]\) \(768\) \(-0.029249\) \(\Gamma_0(N)\)-optimal
5880.x2 5880j2 \([0, 1, 0, 124, 720]\) \(2382032/3645\) \(-320060160\) \([2]\) \(1536\) \(0.31733\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5880.x have rank \(1\).

Complex multiplication

The elliptic curves in class 5880.x do not have complex multiplication.

Modular form 5880.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 2 q^{13} - q^{15} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.