Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 287490cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.cs3 287490cs1 [1, 1, 1, -4820, -83323] [2] 829440 \(\Gamma_0(N)\)-optimal
287490.cs2 287490cs2 [1, 1, 1, -32200, 2150885] [2, 2] 1658880  
287490.cs1 287490cs3 [1, 1, 1, -511350, 140529405] [2] 3317760  
287490.cs4 287490cs4 [1, 1, 1, 8870, 7309277] [2] 3317760  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 287490cs do not have complex multiplication.

Modular form 287490.2.a.cs

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

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 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.