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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 338130.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.r1 | 338130r1 | \([1, -1, 0, -795960, -156528320]\) | \(3169397364769/1231093760\) | \(21662680110975221760\) | \([2]\) | \(7077888\) | \(2.4090\) | \(\Gamma_0(N)\)-optimal |
| 338130.r2 | 338130r2 | \([1, -1, 0, 2533320, -1128012224]\) | \(102181603702751/90336313600\) | \(-1589583772986990393600\) | \([2]\) | \(14155776\) | \(2.7556\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.r have rank \(0\).
Complex multiplication
The elliptic curves in class 338130.r do not have complex multiplication.Modular form 338130.2.a.r
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.
