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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 16758.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16758.v1 | 16758bp3 | \([1, -1, 1, -8004821, 8719166355]\) | \(661397832743623417/443352042\) | \(38024584879769082\) | \([2]\) | \(491520\) | \(2.4976\) | |
| 16758.v2 | 16758bp2 | \([1, -1, 1, -503411, 134552751]\) | \(164503536215257/4178071044\) | \(358336946706300324\) | \([2, 2]\) | \(245760\) | \(2.1510\) | |
| 16758.v3 | 16758bp1 | \([1, -1, 1, -71231, -4263465]\) | \(466025146777/177366672\) | \(15212051452119312\) | \([2]\) | \(122880\) | \(1.8044\) | \(\Gamma_0(N)\)-optimal |
| 16758.v4 | 16758bp4 | \([1, -1, 1, 83119, 428990811]\) | \(740480746823/927484650666\) | \(-79546760774662886586\) | \([2]\) | \(491520\) | \(2.4976\) |
Rank
sage: E.rank()
The elliptic curves in class 16758.v have rank \(1\).
Complex multiplication
The elliptic curves in class 16758.v do not have complex multiplication.Modular form 16758.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
