Properties

Label 5808.l
Number of curves $4$
Conductor $5808$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 5808.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5808.l1 5808p3 \([0, -1, 0, -155888, -23547456]\) \(57736239625/255552\) \(1854365518528512\) \([2]\) \(34560\) \(1.7820\)  
5808.l2 5808p4 \([0, -1, 0, -78448, -47027264]\) \(-7357983625/127552392\) \(-925560189435543552\) \([2]\) \(69120\) \(2.1286\)  
5808.l3 5808p1 \([0, -1, 0, -10688, 404736]\) \(18609625/1188\) \(8620500860928\) \([2]\) \(11520\) \(1.2327\) \(\Gamma_0(N)\)-optimal
5808.l4 5808p2 \([0, -1, 0, 8672, 1690240]\) \(9938375/176418\) \(-1280144377847808\) \([2]\) \(23040\) \(1.5793\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5808.l have rank \(1\).

Complex multiplication

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

Modular form 5808.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.