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Properties

Label 11550.cf
Number of curves $2$
Conductor $11550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 11550.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.cf1 11550co2 \([1, 0, 0, -1176923, -183907563]\) \(1442307535559216746181/717904548395249292\) \(89738068549406161500\) \([2]\) \(351232\) \(2.5215\)  
11550.cf2 11550co1 \([1, 0, 0, -958223, -360835863]\) \(778419129671687951621/693260592493392\) \(86657574061674000\) \([2]\) \(175616\) \(2.1750\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11550.2.a.cf

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.