Properties

Label 5780e
Number of curves 4
Conductor 5780
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5780.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5780e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5780.f3 5780e1 [0, -1, 0, -385, 2130] [2] 2304 \(\Gamma_0(N)\)-optimal
5780.f4 5780e2 [0, -1, 0, 1060, 13112] [2] 4608  
5780.f1 5780e3 [0, -1, 0, -11945, -498418] [2] 6912  
5780.f2 5780e4 [0, -1, 0, -10500, -625000] [2] 13824  

Rank

sage: E.rank()
 

The elliptic curves in class 5780e have rank \(1\).

Modular form 5780.2.a.f

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

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 Cremona 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 Cremona labels.