Properties

Label 482664cn
Number of curves $4$
Conductor $482664$
CM no
Rank $0$
Graph

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

Elliptic curves in class 482664cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
482664.cn3 482664cn1 \([0, 1, 0, -20167, 1095602]\) \(11745974272/357\) \(27570733008\) \([2]\) \(614400\) \(1.1012\) \(\Gamma_0(N)\)-optimal
482664.cn2 482664cn2 \([0, 1, 0, -21012, 997920]\) \(830321872/127449\) \(157484026941696\) \([2, 2]\) \(1228800\) \(1.4478\)  
482664.cn4 482664cn3 \([0, 1, 0, 36448, 5548752]\) \(1083360092/3306177\) \(-16341283736773632\) \([2]\) \(2457600\) \(1.7943\)  
482664.cn1 482664cn4 \([0, 1, 0, -91992, -9791040]\) \(17418812548/1753941\) \(8669120721171456\) \([2]\) \(2457600\) \(1.7943\)  

Rank

sage: E.rank()
 

The elliptic curves in class 482664cn have rank \(0\).

Complex multiplication

The elliptic curves in class 482664cn do not have complex multiplication.

Modular form 482664.2.a.cn

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} - q^{7} + q^{9} + 4 q^{11} + 2 q^{15} + q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.