Properties

Label 22848.cq
Number of curves $2$
Conductor $22848$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cq1 22848cp2 \([0, 1, 0, -1377, 18207]\) \(2204605874/127449\) \(16704995328\) \([2]\) \(20480\) \(0.71547\)  
22848.cq2 22848cp1 \([0, 1, 0, 63, 1215]\) \(415292/9639\) \(-631701504\) \([2]\) \(10240\) \(0.36890\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22848.cq have rank \(0\).

Complex multiplication

The elliptic curves in class 22848.cq do not have complex multiplication.

Modular form 22848.2.a.cq

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} - q^{7} + q^{9} + 6q^{11} + 4q^{13} + 2q^{15} + q^{17} + 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.