Properties

Label 13200.cd
Number of curves $2$
Conductor $13200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 13200.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13200.cd1 13200ch1 \([0, 1, 0, -373, -3037]\) \(-56197120/3267\) \(-334540800\) \([]\) \(5184\) \(0.39194\) \(\Gamma_0(N)\)-optimal
13200.cd2 13200ch2 \([0, 1, 0, 2027, -4477]\) \(8990228480/5314683\) \(-544223539200\) \([]\) \(15552\) \(0.94124\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13200.cd have rank \(0\).

Complex multiplication

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

Modular form 13200.2.a.cd

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.