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Properties

Label 201810.w
Number of curves $4$
Conductor $201810$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 201810.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
201810.w1 201810cb4 [1, 0, 1, -358954, -82806034] [2] 1843200  
201810.w2 201810cb2 [1, 0, 1, -22604, -1274794] [2, 2] 921600  
201810.w3 201810cb1 [1, 0, 1, -3384, 47542] [2] 460800 \(\Gamma_0(N)\)-optimal
201810.w4 201810cb3 [1, 0, 1, 6226, -4296178] [2] 1843200  

Rank

sage: E.rank()
 

The elliptic curves in class 201810.w have rank \(1\).

Complex multiplication

The elliptic curves in class 201810.w do not have complex multiplication.

Modular form 201810.2.a.w

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 LMFDB 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 LMFDB labels.