Properties

Label 5610.i
Number of curves $2$
Conductor $5610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.i1 5610g2 \([1, 1, 0, -185702, -30879084]\) \(708234550511150304361/23696640000\) \(23696640000\) \([2]\) \(28160\) \(1.4903\)  
5610.i2 5610g1 \([1, 1, 0, -11622, -484716]\) \(173629978755828841/1000026931200\) \(1000026931200\) \([2]\) \(14080\) \(1.1437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5610.i have rank \(0\).

Complex multiplication

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

Modular form 5610.2.a.i

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