Properties

Label 960.l
Number of curves 8
Conductor 960
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("960.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 960.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
960.l1 960g7 [0, 1, 0, -138241, -19829665] [2] 2048  
960.l2 960g5 [0, 1, 0, -8641, -311905] [2, 2] 1024  
960.l3 960g8 [0, 1, 0, -7041, -429345] [2] 2048  
960.l4 960g4 [0, 1, 0, -5121, 139359] [2] 512  
960.l5 960g3 [0, 1, 0, -641, -3105] [2, 2] 512  
960.l6 960g2 [0, 1, 0, -321, 2079] [2, 2] 256  
960.l7 960g1 [0, 1, 0, -1, 95] [2] 128 \(\Gamma_0(N)\)-optimal
960.l8 960g6 [0, 1, 0, 2239, -20961] [2] 1024  

Rank

sage: E.rank()
 

The elliptic curves in class 960.l have rank \(0\).

Modular form 960.2.a.l

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

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 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.