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Properties

Label 20622.j
Number of curves $2$
Conductor $20622$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 20622.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20622.j1 20622k2 \([1, 0, 0, -5455771, -5039899603]\) \(-17959412105181401119111729/577896056532732884604\) \(-577896056532732884604\) \([]\) \(998816\) \(2.7595\)  
20622.j2 20622k1 \([1, 0, 0, -32311, 6205097]\) \(-3730574781442415089/14488936015970304\) \(-14488936015970304\) \([7]\) \(142688\) \(1.7865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20622.j have rank \(1\).

Complex multiplication

The elliptic curves in class 20622.j do not have complex multiplication.

Modular form 20622.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} + q^{14} - q^{15} + q^{16} - 3 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.