Properties

Label 13200.cl
Number of curves $4$
Conductor $13200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13200.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13200.cl1 13200cc4 \([0, 1, 0, -6249908, 6011849688]\) \(6749703004355978704/5671875\) \(22687500000000\) \([2]\) \(165888\) \(2.2983\)  
13200.cl2 13200cc3 \([0, 1, 0, -390533, 93880938]\) \(-26348629355659264/24169921875\) \(-6042480468750000\) \([2]\) \(82944\) \(1.9517\)  
13200.cl3 13200cc2 \([0, 1, 0, -78908, 7829688]\) \(13584145739344/1195803675\) \(4783214700000000\) \([2]\) \(55296\) \(1.7490\)  
13200.cl4 13200cc1 \([0, 1, 0, 5467, 573438]\) \(72268906496/606436875\) \(-151609218750000\) \([2]\) \(27648\) \(1.4024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13200.cl have rank \(1\).

Complex multiplication

The elliptic curves in class 13200.cl do not have complex multiplication.

Modular form 13200.2.a.cl

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.