Properties

Label 11200.bk
Number of curves $4$
Conductor $11200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11200.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.bk1 11200bv3 [0, 0, 0, -29900, -1990000] [2] 16384  
11200.bk2 11200bv4 [0, 0, 0, -5900, 138000] [2] 16384  
11200.bk3 11200bv2 [0, 0, 0, -1900, -30000] [2, 2] 8192  
11200.bk4 11200bv1 [0, 0, 0, 100, -2000] [2] 4096 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11200.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 11200.bk do not have complex multiplication.

Modular form 11200.2.a.bk

sage: E.q_eigenform(10)
 
\( q - q^{7} - 3q^{9} - 4q^{11} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.