Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("960.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 960.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
960.p1 960o8 [0, 1, 0, -341345, 76646943] [4] 4608  
960.p2 960o7 [0, 1, 0, -29025, 249375] [2] 4608  
960.p3 960o6 [0, 1, 0, -21345, 1190943] [2, 2] 2304  
960.p4 960o4 [0, 1, 0, -18465, -971937] [2] 1536  
960.p5 960o5 [0, 1, 0, -4385, 94815] [4] 1536  
960.p6 960o2 [0, 1, 0, -1185, -14625] [2, 2] 768  
960.p7 960o3 [0, 1, 0, -865, 31775] [2] 1152  
960.p8 960o1 [0, 1, 0, 95, -1057] [2] 384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 960.2.a.p

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + 4q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.