Properties

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

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 22050do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.fu2 22050do1 \([1, -1, 1, -5375, -63773]\) \(59319/28\) \(8104898434500\) \([2]\) \(55296\) \(1.1711\) \(\Gamma_0(N)\)-optimal
22050.fu1 22050do2 \([1, -1, 1, -71525, -7340273]\) \(139798359/98\) \(28367144520750\) \([2]\) \(110592\) \(1.5177\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22050.2.a.do

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} + 6 q^{11} + 2 q^{13} + q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.