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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 182070.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182070.cw1 | 182070be2 | \([1, -1, 1, -98014838, 373055777381]\) | \(5918043195362419129/8515734343200\) | \(149845312339806907303200\) | \([2]\) | \(35389440\) | \(3.3494\) | |
182070.cw2 | 182070be1 | \([1, -1, 1, -4378838, 9223735781]\) | \(-527690404915129/1782829440000\) | \(-31371179926335661440000\) | \([2]\) | \(17694720\) | \(3.0028\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182070.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 182070.cw do not have complex multiplication.Modular form 182070.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.