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Properties

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

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 11550ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.ct2 11550ct1 \([1, 0, 0, 1737, -3483]\) \(296740963/174636\) \(-341085937500\) \([2]\) \(15360\) \(0.90233\) \(\Gamma_0(N)\)-optimal
11550.ct1 11550ct2 \([1, 0, 0, -7013, -29733]\) \(19530306557/11114334\) \(21707683593750\) \([2]\) \(30720\) \(1.2489\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11550.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - 2 q^{13} + q^{14} + q^{16} - 2 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.