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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 177450.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177450.do1 | 177450hr3 | \([1, 0, 1, -1578126, 762930898]\) | \(5763259856089/5670\) | \(427625109843750\) | \([2]\) | \(3538944\) | \(2.1008\) | |
| 177450.do2 | 177450hr2 | \([1, 0, 1, -99376, 11725898]\) | \(1439069689/44100\) | \(3325973076562500\) | \([2, 2]\) | \(1769472\) | \(1.7542\) | |
| 177450.do3 | 177450hr1 | \([1, 0, 1, -14876, -442102]\) | \(4826809/1680\) | \(126703736250000\) | \([2]\) | \(884736\) | \(1.4076\) | \(\Gamma_0(N)\)-optimal |
| 177450.do4 | 177450hr4 | \([1, 0, 1, 27374, 39610898]\) | \(30080231/9003750\) | \(-679052836464843750\) | \([2]\) | \(3538944\) | \(2.1008\) |
Rank
sage: E.rank()
The elliptic curves in class 177450.do have rank \(0\).
Complex multiplication
The elliptic curves in class 177450.do do not have complex multiplication.Modular form 177450.2.a.do
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.
