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Properties

Label 95550cq
Number of curves $2$
Conductor $95550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 95550cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.cd2 95550cq1 \([1, 1, 0, -10900075, 13846712125]\) \(623295446073461/5458752\) \(1254329519625000000\) \([2]\) \(4423680\) \(2.6396\) \(\Gamma_0(N)\)-optimal
95550.cd1 95550cq2 \([1, 1, 0, -11145075, 13191337125]\) \(666276475992821/58199166792\) \(13373190964671890625000\) \([2]\) \(8847360\) \(2.9862\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95550cq have rank \(0\).

Complex multiplication

The elliptic curves in class 95550cq do not have complex multiplication.

Modular form 95550.2.a.cq

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