Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("240.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 240.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
240.d1 240d7 [0, 1, 0, -34560, 2461428] [4] 256  
240.d2 240d5 [0, 1, 0, -2160, 37908] [2, 4] 128  
240.d3 240d8 [0, 1, 0, -1760, 52788] [4] 256  
240.d4 240d3 [0, 1, 0, -1280, -18060] [2] 64  
240.d5 240d4 [0, 1, 0, -160, 308] [2, 4] 64  
240.d6 240d2 [0, 1, 0, -80, -300] [2, 2] 32  
240.d7 240d1 [0, 1, 0, 0, -12] [2] 16 \(\Gamma_0(N)\)-optimal
240.d8 240d6 [0, 1, 0, 560, 2900] [4] 128  

Rank

sage: E.rank()
 

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

Modular form 240.2.a.d

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.