Properties

Label 4410.a
Number of curves $2$
Conductor $4410$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4410.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.a1 4410b1 \([1, -1, 0, -251085, -48258715]\) \(551105805571803/1376829440\) \(4373530383237120\) \([2]\) \(53760\) \(1.8786\) \(\Gamma_0(N)\)-optimal
4410.a2 4410b2 \([1, -1, 0, -157005, -84931099]\) \(-134745327251163/903920796800\) \(-2871325201213526400\) \([2]\) \(107520\) \(2.2251\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4410.a have rank \(0\).

Complex multiplication

The elliptic curves in class 4410.a do not have complex multiplication.

Modular form 4410.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4 q^{11} - 6 q^{13} + q^{16} - 4 q^{17} - 6 q^{19} + O(q^{20})\) 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.