Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11550.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.cu1 11550cu4 \([1, 0, 0, -6654778, 6606931172]\) \(260744057755293612689909/8504954620259328\) \(1063119327532416000\) \([10]\) \(384000\) \(2.5530\)  
11550.cu2 11550cu3 \([1, 0, 0, -433978, 93753572]\) \(72313087342699809269/11447096545640448\) \(1430887068205056000\) \([10]\) \(192000\) \(2.2064\)  
11550.cu3 11550cu2 \([1, 0, 0, -117753, -15420003]\) \(1444540994277943589/15251205665388\) \(1906400708173500\) \([2]\) \(76800\) \(1.7483\)  
11550.cu4 11550cu1 \([1, 0, 0, -117453, -15503103]\) \(1433528304665250149/162339408\) \(20292426000\) \([2]\) \(38400\) \(1.4017\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11550.2.a.cu

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.