Properties

Label 13200.bi
Number of curves $4$
Conductor $13200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 13200.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13200.bi1 13200bm3 \([0, -1, 0, -58608, -5436288]\) \(347873904937/395307\) \(25299648000000\) \([2]\) \(49152\) \(1.4852\)  
13200.bi2 13200bm2 \([0, -1, 0, -4608, -36288]\) \(169112377/88209\) \(5645376000000\) \([2, 2]\) \(24576\) \(1.1387\)  
13200.bi3 13200bm1 \([0, -1, 0, -2608, 51712]\) \(30664297/297\) \(19008000000\) \([2]\) \(12288\) \(0.79209\) \(\Gamma_0(N)\)-optimal
13200.bi4 13200bm4 \([0, -1, 0, 17392, -300288]\) \(9090072503/5845851\) \(-374134464000000\) \([2]\) \(49152\) \(1.4852\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13200.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{7} + q^{9} - q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.