Properties

Label 59290br
Number of curves $4$
Conductor $59290$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("59290.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 59290br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59290.bc4 59290br1 [1, -1, 0, 13711, -987827] [2] 245760 \(\Gamma_0(N)\)-optimal
59290.bc3 59290br2 [1, -1, 0, -104869, -10545375] [2, 2] 491520  
59290.bc2 59290br3 [1, -1, 0, -519899, 134964143] [2] 983040  
59290.bc1 59290br4 [1, -1, 0, -1587119, -769160925] [2] 983040  

Rank

sage: E.rank()
 

The elliptic curves in class 59290br have rank \(2\).

Modular form 59290.2.a.bc

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - 3q^{9} - q^{10} - 6q^{13} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.