Properties

Label 33600cn
Number of curves $4$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 33600cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.fd4 33600cn1 \([0, 1, 0, 667, -2037]\) \(2048000/1323\) \(-21168000000\) \([2]\) \(27648\) \(0.67022\) \(\Gamma_0(N)\)-optimal
33600.fd3 33600cn2 \([0, 1, 0, -2833, -19537]\) \(9826000/5103\) \(1306368000000\) \([2]\) \(55296\) \(1.0168\)  
33600.fd2 33600cn3 \([0, 1, 0, -11333, -482037]\) \(-10061824000/352947\) \(-5647152000000\) \([2]\) \(82944\) \(1.2195\)  
33600.fd1 33600cn4 \([0, 1, 0, -182833, -30151537]\) \(2640279346000/3087\) \(790272000000\) \([2]\) \(165888\) \(1.5661\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33600cn have rank \(0\).

Complex multiplication

The elliptic curves in class 33600cn do not have complex multiplication.

Modular form 33600.2.a.cn

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.