Properties

Label 18480cd
Number of curves $6$
Conductor $18480$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18480cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18480.bg6 18480cd1 [0, -1, 0, 560, 1480192] [2] 61440 \(\Gamma_0(N)\)-optimal
18480.bg5 18480cd2 [0, -1, 0, -191520, 31752000] [2, 2] 122880  
18480.bg4 18480cd3 [0, -1, 0, -407120, -52590720] [2] 245760  
18480.bg2 18480cd4 [0, -1, 0, -3049200, 2050417152] [2, 4] 245760  
18480.bg1 18480cd5 [0, -1, 0, -48787200, 131177938752] [4] 491520  
18480.bg3 18480cd6 [0, -1, 0, -3034080, 2071742400] [4] 491520  

Rank

sage: E.rank()
 

The elliptic curves in class 18480cd have rank \(0\).

Complex multiplication

The elliptic curves in class 18480cd do not have complex multiplication.

Modular form 18480.2.a.cd

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} - q^{7} + q^{9} + q^{11} - 2q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.