Properties

Label 5775u
Number of curves $6$
Conductor $5775$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5775.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5775u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5775.v4 5775u1 [1, 0, 1, -6626, 207023] [2] 6144 \(\Gamma_0(N)\)-optimal
5775.v3 5775u2 [1, 0, 1, -6751, 198773] [2, 2] 12288  
5775.v2 5775u3 [1, 0, 1, -21876, -1011227] [2, 2] 24576  
5775.v5 5775u4 [1, 0, 1, 6374, 881273] [2] 24576  
5775.v1 5775u5 [1, 0, 1, -331251, -73404977] [2] 49152  
5775.v6 5775u6 [1, 0, 1, 45499, -5996977] [2] 49152  

Rank

sage: E.rank()
 

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

Modular form 5775.2.a.v

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.