Properties

Label 720.e
Number of curves 4
Conductor 720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("720.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 720.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.e1 720d3 [0, 0, 0, -963, -11502] [2] 256  
720.e2 720d2 [0, 0, 0, -63, -162] [2, 2] 128  
720.e3 720d1 [0, 0, 0, -18, 27] [2] 64 \(\Gamma_0(N)\)-optimal
720.e4 720d4 [0, 0, 0, 117, -918] [2] 256  

Rank

sage: E.rank()
 

The elliptic curves in class 720.e have rank \(0\).

Modular form 720.2.a.e

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

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 LMFDB 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 LMFDB labels.