Properties

Label 5808be
Number of curves $2$
Conductor $5808$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 5808be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5808.bf2 5808be1 \([0, 1, 0, -9357, 401850]\) \(-3196715008/649539\) \(-18411167366064\) \([2]\) \(14400\) \(1.2677\) \(\Gamma_0(N)\)-optimal
5808.bf1 5808be2 \([0, 1, 0, -156372, 23747832]\) \(932410994128/29403\) \(13334837269248\) \([2]\) \(28800\) \(1.6143\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5808.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + 2 q^{7} + q^{9} - 6 q^{13} + 2 q^{15} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.