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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 242550.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.p1 | 242550p4 | \([1, -1, 0, -2934757107, 61192659098101]\) | \(260744057755293612689909/8504954620259328\) | \(91179620882583822078336000\) | \([2]\) | \(147456000\) | \(4.0753\) | |
| 242550.p2 | 242550p3 | \([1, -1, 0, -191384307, 868634598901]\) | \(72313087342699809269/11447096545640448\) | \(122721633429010085707776000\) | \([2]\) | \(73728000\) | \(3.7287\) | |
| 242550.p3 | 242550p2 | \([1, -1, 0, -51929082, -142700789624]\) | \(1444540994277943589/15251205665388\) | \(163504593811694089993500\) | \([2]\) | \(29491200\) | \(3.2705\) | |
| 242550.p4 | 242550p1 | \([1, -1, 0, -51796782, -143470643324]\) | \(1433528304665250149/162339408\) | \(1740402663699546000\) | \([2]\) | \(14745600\) | \(2.9240\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.p have rank \(0\).
Complex multiplication
The elliptic curves in class 242550.p do not have complex multiplication.Modular form 242550.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
