Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16800s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16800.bc3 16800s1 \([0, 1, 0, -1758, -28512]\) \(601211584/11025\) \(11025000000\) \([2, 2]\) \(18432\) \(0.72173\) \(\Gamma_0(N)\)-optimal
16800.bc1 16800s2 \([0, 1, 0, -28008, -1813512]\) \(303735479048/105\) \(840000000\) \([2]\) \(36864\) \(1.0683\)  
16800.bc2 16800s3 \([0, 1, 0, -3633, 40863]\) \(82881856/36015\) \(2304960000000\) \([2]\) \(36864\) \(1.0683\)  
16800.bc4 16800s4 \([0, 1, 0, -8, -81012]\) \(-8/354375\) \(-2835000000000\) \([2]\) \(36864\) \(1.0683\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16800.2.a.s

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.