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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 277200.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.dg1 | 277200dg3 | \([0, 0, 0, -348591675, 2505088134250]\) | \(100407751863770656369/166028940000\) | \(7746246224640000000000\) | \([2]\) | \(47185920\) | \(3.4629\) | |
| 277200.dg2 | 277200dg2 | \([0, 0, 0, -21999675, 38338758250]\) | \(25238585142450289/995844326400\) | \(46462112892518400000000\) | \([2, 2]\) | \(23592960\) | \(3.1163\) | |
| 277200.dg3 | 277200dg1 | \([0, 0, 0, -3567675, -1787705750]\) | \(107639597521009/32699842560\) | \(1525643854479360000000\) | \([2]\) | \(11796480\) | \(2.7697\) | \(\Gamma_0(N)\)-optimal |
| 277200.dg4 | 277200dg4 | \([0, 0, 0, 9680325, 139683078250]\) | \(2150235484224911/181905111732960\) | \(-8486964893012981760000000\) | \([2]\) | \(47185920\) | \(3.4629\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.dg do not have complex multiplication.Modular form 277200.2.a.dg
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.
