Properties

Label 287490.ba
Number of curves $4$
Conductor $287490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("287490.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 287490.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.ba1 287490ba4 [1, 1, 0, -16210357, -25127758319] [2] 18210816  
287490.ba2 287490ba3 [1, 1, 0, -1589437, 101805529] [2] 18210816  
287490.ba3 287490ba2 [1, 1, 0, -1014457, -391872299] [2, 2] 9105408  
287490.ba4 287490ba1 [1, 1, 0, -28777, -12779771] [2] 4552704 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 287490.ba have rank \(1\).

Modular form 287490.2.a.ba

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + 4q^{11} - q^{12} - 6q^{13} - q^{14} - q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.