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Properties

Label 189618.j
Number of curves $2$
Conductor $189618$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 189618.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.j1 189618bt1 \([1, 1, 0, -1524, -11760]\) \(81182737/35904\) \(173301750336\) \([2]\) \(207360\) \(0.85223\) \(\Gamma_0(N)\)-optimal
189618.j2 189618bt2 \([1, 1, 0, 5236, -80712]\) \(3288008303/2517768\) \(-12152785242312\) \([2]\) \(414720\) \(1.1988\)  

Rank

sage: E.rank()
 

The elliptic curves in class 189618.j have rank \(1\).

Complex multiplication

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

Modular form 189618.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{8} + q^{9} - 2 q^{10} - q^{11} - q^{12} - 2 q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.