Properties

Label 2646.a
Number of curves $3$
Conductor $2646$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2646.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2646.a1 2646g3 [1, -1, 0, -6036, 240848] [] 6804  
2646.a2 2646g1 [1, -1, 0, -156, -722] [] 756 \(\Gamma_0(N)\)-optimal
2646.a3 2646g2 [1, -1, 0, 579, -3907] [] 2268  

Rank

sage: E.rank()
 

The elliptic curves in class 2646.a have rank \(0\).

Complex multiplication

The elliptic curves in class 2646.a do not have complex multiplication.

Modular form 2646.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 3q^{5} - q^{8} + 3q^{10} - 3q^{11} + 4q^{13} + q^{16} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.