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Properties

Label 5610.e
Number of curves $2$
Conductor $5610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.e1 5610e1 \([1, 1, 0, -88, -308]\) \(76711450249/12622500\) \(12622500\) \([2]\) \(1920\) \(0.084170\) \(\Gamma_0(N)\)-optimal
5610.e2 5610e2 \([1, 1, 0, 162, -1458]\) \(465664585751/1274620050\) \(-1274620050\) \([2]\) \(3840\) \(0.43074\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5610.e have rank \(1\).

Complex multiplication

The elliptic curves in class 5610.e do not have complex multiplication.

Modular form 5610.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - 4 q^{13} - 4 q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.