Properties

Label 720.c
Number of curves 8
Conductor 720
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("720.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 720.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.c1 720h7 [0, 0, 0, -311043, -66769598] [2] 2048  
720.c2 720h5 [0, 0, 0, -19443, -1042958] [2, 2] 1024  
720.c3 720h8 [0, 0, 0, -15843, -1441118] [2] 2048  
720.c4 720h4 [0, 0, 0, -11523, 476098] [2] 512  
720.c5 720h3 [0, 0, 0, -1443, -9758] [2, 2] 512  
720.c6 720h2 [0, 0, 0, -723, 7378] [2, 2] 256  
720.c7 720h1 [0, 0, 0, -3, 322] [2] 128 \(\Gamma_0(N)\)-optimal
720.c8 720h6 [0, 0, 0, 5037, -73262] [2] 1024  

Rank

sage: E.rank()
 

The elliptic curves in class 720.c have rank \(1\).

Modular form 720.2.a.c

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.