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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 48510cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48510.cf1 | 48510cw1 | \([1, -1, 1, -39038, 3006861]\) | \(-76711450249/851840\) | \(-73059012512640\) | \([]\) | \(196560\) | \(1.4751\) | \(\Gamma_0(N)\)-optimal |
48510.cf2 | 48510cw2 | \([1, -1, 1, 130747, 15503037]\) | \(2882081488391/2883584000\) | \(-247313814257664000\) | \([]\) | \(589680\) | \(2.0244\) |
Rank
sage: E.rank()
The elliptic curves in class 48510cw have rank \(0\).
Complex multiplication
The elliptic curves in class 48510cw do not have complex multiplication.Modular form 48510.2.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 Cremona 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 Cremona labels.