Properties

Label 11550.bt
Number of curves $4$
Conductor $11550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 11550.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.bt1 11550bq4 \([1, 1, 1, -6652813, 6601973531]\) \(2084105208962185000201/31185000\) \(487265625000\) \([2]\) \(294912\) \(2.2462\)  
11550.bt2 11550bq3 \([1, 1, 1, -450813, 84609531]\) \(648474704552553481/176469171805080\) \(2757330809454375000\) \([2]\) \(294912\) \(2.2462\)  
11550.bt3 11550bq2 \([1, 1, 1, -415813, 103019531]\) \(508859562767519881/62240270400\) \(972504225000000\) \([2, 2]\) \(147456\) \(1.8997\)  
11550.bt4 11550bq1 \([1, 1, 1, -23813, 1883531]\) \(-95575628340361/43812679680\) \(-684573120000000\) \([4]\) \(73728\) \(1.5531\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11550.bt have rank \(1\).

Complex multiplication

The elliptic curves in class 11550.bt do not have complex multiplication.

Modular form 11550.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} - q^{11} - q^{12} - 2 q^{13} + q^{14} + q^{16} + 2 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.