Properties

Label 287490.bb
Number of curves $2$
Conductor $287490$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("287490.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 287490.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.bb1 287490bb2 [1, 1, 0, -132116742, -584548119126] [2] 61378560  
287490.bb2 287490bb1 [1, 1, 0, -8016892, -9692793956] [2] 30689280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 287490.bb have rank \(0\).

Modular form 287490.2.a.bb

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

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 LMFDB 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 LMFDB labels.