Properties

Label 265200.g
Number of curves 4
Conductor 265200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("265200.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.g1 265200g3 [0, -1, 0, -150924008, 713700550512] [2] 42467328  
265200.g2 265200g2 [0, -1, 0, -9484008, 11026630512] [2, 2] 21233664  
265200.g3 265200g1 [0, -1, 0, -1292008, -311097488] [2] 10616832 \(\Gamma_0(N)\)-optimal
265200.g4 265200g4 [0, -1, 0, 883992, 33836230512] [2] 42467328  

Rank

sage: E.rank()
 

The elliptic curves in class 265200.g have rank \(0\).

Modular form 265200.2.a.g

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.