Properties

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

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 2646.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.n1 2646f1 \([1, -1, 0, -6918, -219752]\) \(-11527859979/28\) \(-88942644\) \([]\) \(3456\) \(0.76559\) \(\Gamma_0(N)\)-optimal
2646.n2 2646f2 \([1, -1, 0, -4713, -363763]\) \(-5000211/21952\) \(-50833922981184\) \([]\) \(10368\) \(1.3149\)  
2646.n3 2646f3 \([1, -1, 0, 41592, 8813888]\) \(381790581/1835008\) \(-38243708913844224\) \([]\) \(31104\) \(1.8642\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2646.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.