Properties

Label 265200.ds
Number of curves 4
Conductor 265200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("265200.ds1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.ds1 265200ds4 [0, -1, 0, -30648008, -65184361488] [2] 26542080  
265200.ds2 265200ds3 [0, -1, 0, -25688008, 49860758512] [2] 26542080  
265200.ds3 265200ds2 [0, -1, 0, -2568008, -263401488] [2, 2] 13271040  
265200.ds4 265200ds1 [0, -1, 0, 631992, -33001488] [2] 6635520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 265200.ds have rank \(1\).

Modular form 265200.2.a.ds

sage: E.q_eigenform(10)
 
\( q - q^{3} + 4q^{7} + q^{9} + 4q^{11} - q^{13} + q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.