Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bs1 189618k2 \([1, 0, 0, -207282, -20993220]\) \(204055591784617/78708537864\) \(379911078938795976\) \([2]\) \(3161088\) \(2.0722\)  
189618.bs2 189618k1 \([1, 0, 0, -92362, 10563812]\) \(18052771191337/444958272\) \(2147728591914048\) \([2]\) \(1580544\) \(1.7257\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.bs

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} + 2q^{14} + 2q^{15} + q^{16} - q^{17} + q^{18} - 6q^{19} + O(q^{20})\)  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.