Properties

Label 5775.y
Number of curves $2$
Conductor $5775$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 5775.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5775.y1 5775f2 \([0, -1, 1, -669758, -3988338457]\) \(-2126464142970105856/438611057788643355\) \(-6853297777947552421875\) \([]\) \(720000\) \(2.8692\)  
5775.y2 5775f1 \([0, -1, 1, -223508, 47704043]\) \(-79028701534867456/16987307596875\) \(-265426681201171875\) \([]\) \(144000\) \(2.0645\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5775.y have rank \(0\).

Complex multiplication

The elliptic curves in class 5775.y do not have complex multiplication.

Modular form 5775.2.a.y

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} - q^{7} + q^{9} + q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{14} - 4 q^{16} + 7 q^{17} + 2 q^{18} - 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.