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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 128576.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 128576.dd1 | 128576dc2 | \([0, 0, 0, -30141076588, -2014124231133616]\) | \(98191033604529537629349729/10906239337336\) | \(336359103344998629769216\) | \([]\) | \(227598336\) | \(4.3834\) | |
| 128576.dd2 | 128576dc1 | \([0, 0, 0, -60690028, 167515728464]\) | \(801581275315909089/70810888830976\) | \(2183877167697230672429056\) | \([]\) | \(32514048\) | \(3.4105\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 128576.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 128576.dd do not have complex multiplication.Modular form 128576.2.a.dd
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
