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SageMath
E = EllipticCurve("cw1")
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)
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.