Properties

Label 27200cl
Number of curves 4
Conductor 27200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("27200.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27200cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27200.ci4 27200cl1 [0, -1, 0, -4833, -78463] [2] 55296 \(\Gamma_0(N)\)-optimal
27200.ci3 27200cl2 [0, -1, 0, -68833, -6926463] [2] 110592  
27200.ci2 27200cl3 [0, -1, 0, -164833, 25809537] [2] 165888  
27200.ci1 27200cl4 [0, -1, 0, -180833, 20513537] [2] 331776  

Rank

sage: E.rank()
 

The elliptic curves in class 27200cl have rank \(1\).

Modular form 27200.2.a.ci

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - 4q^{7} + q^{9} + 6q^{11} + 2q^{13} + q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.