Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("265200.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.k1 265200k3 [0, -1, 0, -2959008, 1947856512] [2] 12386304  
265200.k2 265200k2 [0, -1, 0, -307008, -14623488] [2, 2] 6193152  
265200.k3 265200k1 [0, -1, 0, -235008, -43711488] [2] 3096576 \(\Gamma_0(N)\)-optimal
265200.k4 265200k4 [0, -1, 0, 1192992, -116623488] [4] 12386304  

Rank

sage: E.rank()
 

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

Modular form 265200.2.a.k

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.