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Properties

Label 189618w
Number of curves $2$
Conductor $189618$
CM no
Rank $0$
Graph

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

Elliptic curves in class 189618w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
189618.m1 189618w1 [1, 0, 1, -33128, -2322058] [2] 903168 \(\Gamma_0(N)\)-optimal
189618.m2 189618w2 [1, 0, 1, -26368, -3295498] [2] 1806336  

Rank

sage: E.rank()
 

The elliptic curves in class 189618w have rank \(0\).

Complex multiplication

The elliptic curves in class 189618w do not have complex multiplication.

Modular form 189618.2.a.w

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.