Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("11200.bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11200.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.bt1 11200p3 [0, 0, 0, -428300, -107882000] [2] 73728  
11200.bt2 11200p4 [0, 0, 0, -140300, 18902000] [2] 73728  
11200.bt3 11200p2 [0, 0, 0, -28300, -1482000] [2, 2] 36864  
11200.bt4 11200p1 [0, 0, 0, 3700, -138000] [2] 18432 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 11200.2.a.bt

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

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.