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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 33640h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33640.e3 | 33640h1 | \([0, 0, 0, -1682, 24389]\) | \(55296/5\) | \(47585865680\) | \([2]\) | \(25088\) | \(0.78829\) | \(\Gamma_0(N)\)-optimal |
| 33640.e2 | 33640h2 | \([0, 0, 0, -5887, -146334]\) | \(148176/25\) | \(3806869254400\) | \([2, 2]\) | \(50176\) | \(1.1349\) | |
| 33640.e4 | 33640h3 | \([0, 0, 0, 10933, -829226]\) | \(237276/625\) | \(-380686925440000\) | \([2]\) | \(100352\) | \(1.4814\) | |
| 33640.e1 | 33640h4 | \([0, 0, 0, -89987, -10389714]\) | \(132304644/5\) | \(3045495403520\) | \([2]\) | \(100352\) | \(1.4814\) |
Rank
sage: E.rank()
The elliptic curves in class 33640h have rank \(1\).
Complex multiplication
The elliptic curves in class 33640h do not have complex multiplication.Modular form 33640.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
