Properties

Label 22050eg
Number of curves $2$
Conductor $22050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.dt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.dt1 22050eg1 [1, -1, 1, -165605, -9872103] [2] 258048 \(\Gamma_0(N)\)-optimal
22050.dt2 22050eg2 [1, -1, 1, 606145, -76242603] [2] 516096  

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.dt

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} - 2q^{11} + 2q^{13} + q^{16} + 4q^{17} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.