Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 22050.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.q1 22050y2 \([1, -1, 0, -160092, 24820816]\) \(-16591834777/98304\) \(-2688505344000000\) \([]\) \(155520\) \(1.8009\)  
22050.q2 22050y1 \([1, -1, 0, 5283, 179941]\) \(596183/864\) \(-23629441500000\) \([]\) \(51840\) \(1.2516\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22050.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 3 q^{11} + 4 q^{13} + q^{16} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.