Properties

Label 133200ck
Number of curves $3$
Conductor $133200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 133200ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
133200.cw3 133200ck1 \([0, 0, 0, -12000, 502000]\) \(4096000/37\) \(1726272000000\) \([]\) \(207360\) \(1.1706\) \(\Gamma_0(N)\)-optimal
133200.cw2 133200ck2 \([0, 0, 0, -84000, -9074000]\) \(1404928000/50653\) \(2363266368000000\) \([]\) \(622080\) \(1.7199\)  
133200.cw1 133200ck3 \([0, 0, 0, -6744000, -6741002000]\) \(727057727488000/37\) \(1726272000000\) \([]\) \(1866240\) \(2.2693\)  

Rank

sage: E.rank()
 

The elliptic curves in class 133200ck have rank \(1\).

Complex multiplication

The elliptic curves in class 133200ck do not have complex multiplication.

Modular form 133200.2.a.ck

sage: E.q_eigenform(10)
 
\(q - q^{7} + 3 q^{11} + 4 q^{13} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.