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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 35520.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.cg1 | 35520cn4 | \([0, 1, 0, -671201, 94254495]\) | \(127568139540190201/59114336463360\) | \(15496468617851043840\) | \([2]\) | \(1161216\) | \(2.3769\) | |
| 35520.cg2 | 35520cn2 | \([0, 1, 0, -340001, -76417185]\) | \(16581570075765001/998001000\) | \(261619974144000\) | \([2]\) | \(387072\) | \(1.8276\) | |
| 35520.cg3 | 35520cn1 | \([0, 1, 0, -20001, -1345185]\) | \(-3375675045001/999000000\) | \(-261881856000000\) | \([2]\) | \(193536\) | \(1.4810\) | \(\Gamma_0(N)\)-optimal |
| 35520.cg4 | 35520cn3 | \([0, 1, 0, 147999, 11187615]\) | \(1367594037332999/995878502400\) | \(-261063574133145600\) | \([2]\) | \(580608\) | \(2.0303\) |
Rank
sage: E.rank()
The elliptic curves in class 35520.cg have rank \(1\).
Complex multiplication
The elliptic curves in class 35520.cg do not have complex multiplication.Modular form 35520.2.a.cg
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
