Properties

Label 22050.eh
Number of curves $4$
Conductor $22050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.eh1 22050da3 [1, -1, 1, -514730, 124681897] [2] 331776  
22050.eh2 22050da1 [1, -1, 1, -128855, -17748853] [2] 110592 \(\Gamma_0(N)\)-optimal
22050.eh3 22050da2 [1, -1, 1, -92105, -28112353] [2] 221184  
22050.eh4 22050da4 [1, -1, 1, 808270, 659173897] [2] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 22050.eh have rank \(1\).

Modular form 22050.2.a.eh

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.