Properties

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

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Show commands: SageMath
E = EllipticCurve("eg1")
 
E.isogeny_class()
 

Elliptic curves in class 22050eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.dt1 22050eg1 \([1, -1, 1, -165605, -9872103]\) \(1092727/540\) \(248212514556562500\) \([2]\) \(258048\) \(2.0308\) \(\Gamma_0(N)\)-optimal
22050.dt2 22050eg2 \([1, -1, 1, 606145, -76242603]\) \(53582633/36450\) \(-16754344732567968750\) \([2]\) \(516096\) \(2.3774\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 22050eg do not have complex multiplication.

Modular form 22050.2.a.eg

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