Properties

Label 11200co
Number of curves 6
Conductor 11200
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11200.cz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11200co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.cz5 11200co1 [0, -1, 0, -833, -18463] [2] 9216 \(\Gamma_0(N)\)-optimal
11200.cz4 11200co2 [0, -1, 0, -16833, -834463] [2] 18432  
11200.cz6 11200co3 [0, -1, 0, 7167, 389537] [2] 27648  
11200.cz3 11200co4 [0, -1, 0, -56833, 4293537] [2] 55296  
11200.cz2 11200co5 [0, -1, 0, -272833, 55101537] [2] 82944  
11200.cz1 11200co6 [0, -1, 0, -4368833, 3516221537] [2] 165888  

Rank

sage: E.rank()
 

The elliptic curves in class 11200co have rank \(1\).

Modular form 11200.2.a.cz

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.