Properties

Label 203280.cu
Number of curves 8
Conductor 203280
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("203280.cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.cu1 203280cy8 [0, -1, 0, -3718668840, -87281701302288] [2] 62914560  
203280.cu2 203280cy6 [0, -1, 0, -232416840, -1363718012688] [2, 2] 31457280  
203280.cu3 203280cy7 [0, -1, 0, -230964840, -1381599683088] [2] 62914560  
203280.cu4 203280cy3 [0, -1, 0, -29175560, 60649474800] [2] 15728640  
203280.cu5 203280cy4 [0, -1, 0, -14616840, -21024572688] [2, 2] 15728640  
203280.cu6 203280cy2 [0, -1, 0, -2071560, 673743600] [2, 2] 7864320  
203280.cu7 203280cy1 [0, -1, 0, 406520, 75039472] [2] 3932160 \(\Gamma_0(N)\)-optimal
203280.cu8 203280cy5 [0, -1, 0, 2458680, -67224099600] [2] 31457280  

Rank

sage: E.rank()
 

The elliptic curves in class 203280.cu have rank \(0\).

Modular form 203280.2.a.cu

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

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.