Properties

Label 59290.by
Number of curves 4
Conductor 59290
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("59290.by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 59290.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59290.by1 59290cd4 [1, 1, 0, -154841887, -720668834871] [2] 19906560  
59290.by2 59290cd2 [1, 1, 0, -21202227, 37234215341] [2] 6635520  
59290.by3 59290cd1 [1, 1, 0, -332147, 1433680109] [2] 3317760 \(\Gamma_0(N)\)-optimal
59290.by4 59290cd3 [1, 1, 0, 2988093, -38622359299] [2] 9953280  

Rank

sage: E.rank()
 

The elliptic curves in class 59290.by have rank \(0\).

Modular form 59290.2.a.by

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} + q^{5} - 2q^{6} - q^{8} + q^{9} - q^{10} + 2q^{12} - 4q^{13} + 2q^{15} + q^{16} - q^{18} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.