Properties

Label 203280.dg
Number of curves 8
Conductor 203280
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("203280.dg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.dg1 203280ck8 [0, -1, 0, -679986160, -6824703694400] [2] 39813120  
203280.dg2 203280ck6 [0, -1, 0, -42500080, -106620388928] [2, 2] 19906560  
203280.dg3 203280ck7 [0, -1, 0, -39402480, -122824554048] [2] 39813120  
203280.dg4 203280ck5 [0, -1, 0, -8436160, -9262534400] [2] 13271040  
203280.dg5 203280ck3 [0, -1, 0, -2850800, -1407059520] [2] 9953280  
203280.dg6 203280ck2 [0, -1, 0, -1118080, 239260672] [2, 2] 6635520  
203280.dg7 203280ck1 [0, -1, 0, -963200, 364032000] [2] 3317760 \(\Gamma_0(N)\)-optimal
203280.dg8 203280ck4 [0, -1, 0, 3721920, 1753212672] [2] 13271040  

Rank

sage: E.rank()
 

The elliptic curves in class 203280.dg have rank \(1\).

Modular form 203280.2.a.dg

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + q^{7} + q^{9} - 2q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.