Properties

Label 5775.t
Number of curves 6
Conductor 5775
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5775.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5775.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5775.t1 5775n5 [1, 0, 1, -112976, -14625277] [2] 20480  
5775.t2 5775n3 [1, 0, 1, -7101, -226277] [2, 2] 10240  
5775.t3 5775n2 [1, 0, 1, -976, 6473] [2, 2] 5120  
5775.t4 5775n1 [1, 0, 1, -851, 9473] [2] 2560 \(\Gamma_0(N)\)-optimal
5775.t5 5775n6 [1, 0, 1, 774, -698777] [2] 20480  
5775.t6 5775n4 [1, 0, 1, 3149, 47723] [2] 10240  

Rank

sage: E.rank()
 

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

Modular form 5775.2.a.t

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.