Properties

Label 18480ct
Number of curves 4
Conductor 18480
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18480.cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18480ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18480.cj3 18480ct1 [0, 1, 0, -8016, 237204] [2] 36864 \(\Gamma_0(N)\)-optimal
18480.cj2 18480ct2 [0, 1, 0, -33936, -2178540] [2, 2] 73728  
18480.cj1 18480ct3 [0, 1, 0, -527856, -147786156] [2] 147456  
18480.cj4 18480ct4 [0, 1, 0, 45264, -10763820] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 18480ct have rank \(1\).

Modular form 18480.2.a.cj

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.