Properties

Label 11550.cl
Number of curves $4$
Conductor $11550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 11550.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.cl1 11550ci3 \([1, 0, 0, -304588, 64388792]\) \(200005594092187129/1027287538200\) \(16051367784375000\) \([2]\) \(147456\) \(1.9555\)  
11550.cl2 11550ci2 \([1, 0, 0, -29588, -236208]\) \(183337554283129/104587560000\) \(1634180625000000\) \([2, 2]\) \(73728\) \(1.6090\)  
11550.cl3 11550ci1 \([1, 0, 0, -21588, -1220208]\) \(71210194441849/165580800\) \(2587200000000\) \([2]\) \(36864\) \(1.2624\) \(\Gamma_0(N)\)-optimal
11550.cl4 11550ci4 \([1, 0, 0, 117412, -1853208]\) \(11456208593737991/6725709375000\) \(-105089208984375000\) \([2]\) \(147456\) \(1.9555\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11550.cl have rank \(0\).

Complex multiplication

The elliptic curves in class 11550.cl do not have complex multiplication.

Modular form 11550.2.a.cl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + q^{11} + q^{12} + 6 q^{13} - q^{14} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

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.