Properties

Label 22050.bm
Number of curves $4$
Conductor $22050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.bm1 22050d3 [1, -1, 0, -1159692, 480378716] [2] 331776  
22050.bm2 22050d4 [1, -1, 0, -828942, 759862466] [2] 663552  
22050.bm3 22050d1 [1, -1, 0, -57192, -4598784] [2] 110592 \(\Gamma_0(N)\)-optimal
22050.bm4 22050d2 [1, -1, 0, 89808, -24443784] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 22050.bm have rank \(0\).

Modular form 22050.2.a.bm

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} + 2q^{13} + q^{16} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.