Properties

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

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

Elliptic curves in class 5808.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5808.f1 5808f4 \([0, -1, 0, -85224, 9604608]\) \(37736227588/33\) \(59864589312\) \([4]\) \(23040\) \(1.3683\)  
5808.f2 5808f3 \([0, -1, 0, -12624, -332880]\) \(122657188/43923\) \(79679768374272\) \([2]\) \(23040\) \(1.3683\)  
5808.f3 5808f2 \([0, -1, 0, -5364, 149184]\) \(37642192/1089\) \(493882861824\) \([2, 2]\) \(11520\) \(1.0217\)  
5808.f4 5808f1 \([0, -1, 0, 81, 7614]\) \(2048/891\) \(-25255373616\) \([2]\) \(5760\) \(0.67512\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 5808.f do not have complex multiplication.

Modular form 5808.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + 4 q^{7} + q^{9} - 6 q^{13} + 2 q^{15} - 6 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.