Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5775f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5775.y2 5775f1 [0, -1, 1, -223508, 47704043] [] 144000 \(\Gamma_0(N)\)-optimal
5775.y1 5775f2 [0, -1, 1, -669758, -3988338457] [] 720000  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5775.2.a.f

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.