Properties

Label 16800.x
Number of curves $4$
Conductor $16800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16800.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16800.x1 16800j3 \([0, -1, 0, -28008, 1813512]\) \(303735479048/105\) \(840000000\) \([2]\) \(36864\) \(1.0683\)  
16800.x2 16800j2 \([0, -1, 0, -3633, -40863]\) \(82881856/36015\) \(2304960000000\) \([2]\) \(36864\) \(1.0683\)  
16800.x3 16800j1 \([0, -1, 0, -1758, 28512]\) \(601211584/11025\) \(11025000000\) \([2, 2]\) \(18432\) \(0.72173\) \(\Gamma_0(N)\)-optimal
16800.x4 16800j4 \([0, -1, 0, -8, 81012]\) \(-8/354375\) \(-2835000000000\) \([2]\) \(36864\) \(1.0683\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16800.x have rank \(0\).

Complex multiplication

The elliptic curves in class 16800.x do not have complex multiplication.

Modular form 16800.2.a.x

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.