Properties

Label 51600.bg
Number of curves $2$
Conductor $51600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 51600.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.bg1 51600cf1 \([0, -1, 0, -3208, -115088]\) \(-2282665/2322\) \(-3715200000000\) \([]\) \(86400\) \(1.1075\) \(\Gamma_0(N)\)-optimal
51600.bg2 51600cf2 \([0, -1, 0, 26792, 2044912]\) \(1329238535/1908168\) \(-3053068800000000\) \([]\) \(259200\) \(1.6568\)  

Rank

sage: E.rank()
 

The elliptic curves in class 51600.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 51600.bg do not have complex multiplication.

Modular form 51600.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 4q^{13} - 6q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.