Properties

Label 188760.bg
Number of curves $2$
Conductor $188760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 188760.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.bg1 188760w2 \([0, -1, 0, -517920, 100698732]\) \(4234737878642/1247410125\) \(4525799687076096000\) \([2]\) \(2457600\) \(2.2855\)  
188760.bg2 188760w1 \([0, -1, 0, 87080, 10432732]\) \(40254822716/49359375\) \(-89541779184000000\) \([2]\) \(1228800\) \(1.9389\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 188760.bg do not have complex multiplication.

Modular form 188760.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2q^{7} + q^{9} + q^{13} - q^{15} - 2q^{19} + O(q^{20})\)  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.