Properties

Label 206400.ft
Number of curves $4$
Conductor $206400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ft1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 206400.ft

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206400.ft1 206400gh3 [0, 1, 0, -1341633, 593608863] [2] 3538944  
206400.ft2 206400gh2 [0, 1, 0, -141633, -5191137] [2, 2] 1769472  
206400.ft3 206400gh1 [0, 1, 0, -109633, -13991137] [2] 884736 \(\Gamma_0(N)\)-optimal
206400.ft4 206400gh4 [0, 1, 0, 546367, -40279137] [2] 3538944  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 206400.2.a.ft

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.