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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 720g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 720.g4 | 720g1 | \([0, 0, 0, 93, -94]\) | \(804357/500\) | \(-55296000\) | \([2]\) | \(192\) | \(0.17479\) | \(\Gamma_0(N)\)-optimal |
| 720.g3 | 720g2 | \([0, 0, 0, -387, -766]\) | \(57960603/31250\) | \(3456000000\) | \([2]\) | \(384\) | \(0.52136\) | |
| 720.g2 | 720g3 | \([0, 0, 0, -1107, 16146]\) | \(-1860867/320\) | \(-25798901760\) | \([2]\) | \(576\) | \(0.72409\) | |
| 720.g1 | 720g4 | \([0, 0, 0, -18387, 959634]\) | \(8527173507/200\) | \(16124313600\) | \([2]\) | \(1152\) | \(1.0707\) |
Rank
sage: E.rank()
The elliptic curves in class 720g have rank \(1\).
Complex multiplication
The elliptic curves in class 720g do not have complex multiplication.Modular form 720.2.a.g
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
