Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cw1 22848cq1 \([0, 1, 0, -11989, -521101]\) \(-11632923639808/318495051\) \(-5218222915584\) \([]\) \(55296\) \(1.2215\) \(\Gamma_0(N)\)-optimal
22848.cw2 22848cq2 \([0, 1, 0, 53291, -2068237]\) \(1021544365555712/705905647251\) \(-11565558124560384\) \([]\) \(165888\) \(1.7708\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.cw

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.