Properties

Label 13200bm
Number of curves 4
Conductor 13200
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("13200.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13200bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13200.bi3 13200bm1 [0, -1, 0, -2608, 51712] [2] 12288 \(\Gamma_0(N)\)-optimal
13200.bi2 13200bm2 [0, -1, 0, -4608, -36288] [2, 2] 24576  
13200.bi1 13200bm3 [0, -1, 0, -58608, -5436288] [2] 49152  
13200.bi4 13200bm4 [0, -1, 0, 17392, -300288] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 13200bm have rank \(0\).

Modular form 13200.2.a.bi

sage: E.q_eigenform(10)
 
\( q - q^{3} + 4q^{7} + q^{9} - q^{11} + 2q^{13} + 2q^{17} + O(q^{20}) \)

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 Cremona 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 Cremona labels.