Properties

Label 5808.t
Number of curves 4
Conductor 5808
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5808.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5808.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5808.t1 5808bg3 [0, 1, 0, -283664, 57999060] [2] 46080  
5808.t2 5808bg2 [0, 1, 0, -22304, 395316] [2, 2] 23040  
5808.t3 5808bg1 [0, 1, 0, -12624, -545580] [2] 11520 \(\Gamma_0(N)\)-optimal
5808.t4 5808bg4 [0, 1, 0, 84176, 3163796] [4] 46080  

Rank

sage: E.rank()
 

The elliptic curves in class 5808.t have rank \(0\).

Modular form 5808.2.a.t

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + 4q^{7} + q^{9} + 2q^{13} - 2q^{15} + 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.