Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("11550.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11550.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11550.bd1 11550z3 [1, 0, 1, -824776, 288232448] [2] 147456  
11550.bd2 11550z2 [1, 0, 1, -53026, 4228448] [2, 2] 73728  
11550.bd3 11550z1 [1, 0, 1, -12526, -469552] [2] 36864 \(\Gamma_0(N)\)-optimal
11550.bd4 11550z4 [1, 0, 1, 70724, 21058448] [2] 147456  

Rank

sage: E.rank()
 

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

Modular form 11550.2.a.bd

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.