Properties

Label 5610.t
Number of curves $4$
Conductor $5610$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5610.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5610.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.t1 5610r4 [1, 0, 1, -2417353, -1087483252] [2] 276480  
5610.t2 5610r2 [1, 0, 1, -829978, 290863148] [6] 92160  
5610.t3 5610r1 [1, 0, 1, -43898, 5987756] [6] 46080 \(\Gamma_0(N)\)-optimal
5610.t4 5610r3 [1, 0, 1, 367927, -108178804] [2] 138240  

Rank

sage: E.rank()
 

The elliptic curves in class 5610.t have rank \(0\).

Modular form 5610.2.a.t

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 4q^{13} - 2q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.