Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("287490.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 287490b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.b4 287490b1 [1, 1, 0, 109492, 11384448] [2] 3502080 \(\Gamma_0(N)\)-optimal
287490.b3 287490b2 [1, 1, 0, -575008, 102696748] [2, 2] 7004160  
287490.b1 287490b3 [1, 1, 0, -8172958, 8987739478] [2] 14008320  
287490.b2 287490b4 [1, 1, 0, -3929058, -2924668782] [2] 14008320  

Rank

sage: E.rank()
 

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

Modular form 287490.2.a.b

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

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 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.