Properties

Label 199920ch
Number of curves $2$
Conductor $199920$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 199920ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
199920.cv2 199920ch1 \([0, -1, 0, 63880, 7398000]\) \(59822347031/83966400\) \(-40462594021785600\) \([2]\) \(1327104\) \(1.8722\) \(\Gamma_0(N)\)-optimal
199920.cv1 199920ch2 \([0, -1, 0, -406520, 73630320]\) \(15417797707369/4080067320\) \(1966144881175265280\) \([2]\) \(2654208\) \(2.2188\)  

Rank

sage: E.rank()
 

The elliptic curves in class 199920ch have rank \(0\).

Complex multiplication

The elliptic curves in class 199920ch do not have complex multiplication.

Modular form 199920.2.a.ch

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 2q^{11} + 2q^{13} - q^{15} - q^{17} - 4q^{19} + O(q^{20})\)  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.