Properties

Label 203280.ds
Number of curves $2$
Conductor $203280$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ds1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.ds1 203280cq2 [0, -1, 0, -51866085, -2718075836595] [] 144000000  
203280.ds2 203280cq1 [0, -1, 0, -17308485, 32463967725] [] 28800000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 203280.ds do not have complex multiplication.

Modular form 203280.2.a.ds

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

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.