Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.g1 189618bo1 \([1, 1, 0, -14253125, -20716222899]\) \(66342819962001390625/4812668669952\) \(23229832450142343168\) \([2]\) \(9934848\) \(2.7672\) \(\Gamma_0(N)\)-optimal
189618.g2 189618bo2 \([1, 1, 0, -13333765, -23503170803]\) \(-54315282059491182625/17983956399469632\) \(-86805122604567614964288\) \([2]\) \(19869696\) \(3.1137\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.g

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