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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 168200.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 168200.n1 | 168200u4 | \([0, 0, 0, -2249675, -1298714250]\) | \(132304644/5\) | \(47585865680000000\) | \([2]\) | \(2408448\) | \(2.2862\) | |
| 168200.n2 | 168200u2 | \([0, 0, 0, -147175, -18291750]\) | \(148176/25\) | \(59482332100000000\) | \([2, 2]\) | \(1204224\) | \(1.9396\) | |
| 168200.n3 | 168200u1 | \([0, 0, 0, -42050, 3048625]\) | \(55296/5\) | \(743529151250000\) | \([2]\) | \(602112\) | \(1.5930\) | \(\Gamma_0(N)\)-optimal |
| 168200.n4 | 168200u3 | \([0, 0, 0, 273325, -103653250]\) | \(237276/625\) | \(-5948233210000000000\) | \([2]\) | \(2408448\) | \(2.2862\) |
Rank
sage: E.rank()
The elliptic curves in class 168200.n have rank \(1\).
Complex multiplication
The elliptic curves in class 168200.n do not have complex multiplication.Modular form 168200.2.a.n
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.
