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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 966.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 966.g1 | 966g5 | \([1, 1, 1, -79134, -8601153]\) | \(54804145548726848737/637608031452\) | \(637608031452\) | \([2]\) | \(4096\) | \(1.4160\) | |
| 966.g2 | 966g4 | \([1, 1, 1, -17714, 900047]\) | \(614716917569296417/19093020912\) | \(19093020912\) | \([8]\) | \(2048\) | \(1.0694\) | |
| 966.g3 | 966g3 | \([1, 1, 1, -5074, -128689]\) | \(14447092394873377/1439452851984\) | \(1439452851984\) | \([2, 2]\) | \(2048\) | \(1.0694\) | |
| 966.g4 | 966g2 | \([1, 1, 1, -1154, 12431]\) | \(169967019783457/26337394944\) | \(26337394944\) | \([2, 4]\) | \(1024\) | \(0.72283\) | |
| 966.g5 | 966g1 | \([1, 1, 1, 126, 1167]\) | \(221115865823/664731648\) | \(-664731648\) | \([4]\) | \(512\) | \(0.37625\) | \(\Gamma_0(N)\)-optimal |
| 966.g6 | 966g6 | \([1, 1, 1, 6266, -609505]\) | \(27207619911317663/177609314617308\) | \(-177609314617308\) | \([2]\) | \(4096\) | \(1.4160\) |
Rank
sage: E.rank()
The elliptic curves in class 966.g have rank \(1\).
Complex multiplication
The elliptic curves in class 966.g do not have complex multiplication.Modular form 966.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
