Properties

Label 206400.bg
Number of curves $2$
Conductor $206400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 206400.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206400.bg1 206400ed2 \([0, -1, 0, -380033, 87419937]\) \(1481933914201/53916840\) \(220843376640000000\) \([2]\) \(2654208\) \(2.0977\)  
206400.bg2 206400ed1 \([0, -1, 0, -60033, -3780063]\) \(5841725401/1857600\) \(7608729600000000\) \([2]\) \(1327104\) \(1.7512\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 206400.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 206400.bg do not have complex multiplication.

Modular form 206400.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} - 2q^{11} - 2q^{13} + 4q^{17} - 6q^{19} + O(q^{20})\)  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.