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Properties

Label 189618.bj
Number of curves $2$
Conductor $189618$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 189618.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bj1 189618b1 \([1, 0, 0, -15805, -546079]\) \(90458382169/25788048\) \(124473982178832\) \([2]\) \(1075200\) \(1.4112\) \(\Gamma_0(N)\)-optimal
189618.bj2 189618b2 \([1, 0, 0, 41655, -3591459]\) \(1656015369191/2114999172\) \(-10208697038402148\) \([2]\) \(2150400\) \(1.7578\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.bj

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