Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.a1 5610c2 \([1, 1, 0, -719108, -234128688]\) \(41125104693338423360329/179205840000000000\) \(179205840000000000\) \([2]\) \(99840\) \(2.1636\)  
5610.a2 5610c1 \([1, 1, 0, -22788, -7267632]\) \(-1308796492121439049/22000592486400000\) \(-22000592486400000\) \([2]\) \(49920\) \(1.8170\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5610.2.a.a

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