Properties

Label 206400bb
Number of curves $2$
Conductor $206400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 206400bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206400.fo2 206400bb1 [0, 1, 0, -16409633, 26526208863] [2] 23224320 \(\Gamma_0(N)\)-optimal
206400.fo1 206400bb2 [0, 1, 0, -265241633, 1662596608863] [2] 46448640  

Rank

sage: E.rank()
 

The elliptic curves in class 206400bb have rank \(0\).

Complex multiplication

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

Modular form 206400.2.a.bb

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

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 Cremona 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 Cremona labels.