Properties

Label 10944cn
Number of curves $3$
Conductor $10944$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10944cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10944.cl3 10944cn1 \([0, 0, 0, 24, -2]\) \(32768/19\) \(-886464\) \([]\) \(1152\) \(-0.16929\) \(\Gamma_0(N)\)-optimal
10944.cl2 10944cn2 \([0, 0, 0, -336, -2522]\) \(-89915392/6859\) \(-320013504\) \([]\) \(3456\) \(0.38001\)  
10944.cl1 10944cn3 \([0, 0, 0, -27696, -1774082]\) \(-50357871050752/19\) \(-886464\) \([]\) \(10368\) \(0.92932\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10944cn have rank \(0\).

Complex multiplication

The elliptic curves in class 10944cn do not have complex multiplication.

Modular form 10944.2.a.cn

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