Properties

Label 240.b
Number of curves 8
Conductor 240
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("240.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 240.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
240.b1 240b8 [0, -1, 0, -85336, 9623536] [2] 576  
240.b2 240b7 [0, -1, 0, -7256, 34800] [2] 576  
240.b3 240b6 [0, -1, 0, -5336, 151536] [2, 2] 288  
240.b4 240b4 [0, -1, 0, -4616, -119184] [2] 192  
240.b5 240b5 [0, -1, 0, -1096, 12400] [2] 192  
240.b6 240b2 [0, -1, 0, -296, -1680] [2, 2] 96  
240.b7 240b3 [0, -1, 0, -216, 4080] [2] 144  
240.b8 240b1 [0, -1, 0, 24, -144] [2] 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 240.b have rank \(0\).

Modular form 240.2.a.b

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.