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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 165312.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 165312.cs1 | 165312eg2 | \([0, 0, 0, -5536116108, 158546222275824]\) | \(98191033604529537629349729/10906239337336\) | \(2084214794333177511936\) | \([]\) | \(66382848\) | \(3.9598\) | |
| 165312.cs2 | 165312eg1 | \([0, 0, 0, -11147148, -13186369296]\) | \(801581275315909089/70810888830976\) | \(13532171588804674584576\) | \([]\) | \(9483264\) | \(2.9868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 165312.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 165312.cs do not have complex multiplication.Modular form 165312.2.a.cs
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.
