Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 228888u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 228888.bz3 | 228888u1 | \([0, 0, 0, -32079, 2132242]\) | \(810448/33\) | \(148653439342848\) | \([2]\) | \(589824\) | \(1.4852\) | \(\Gamma_0(N)\)-optimal |
| 228888.bz2 | 228888u2 | \([0, 0, 0, -84099, -6534290]\) | \(3650692/1089\) | \(19622253993255936\) | \([2, 2]\) | \(1179648\) | \(1.8318\) | |
| 228888.bz4 | 228888u3 | \([0, 0, 0, 228021, -43676570]\) | \(36382894/43923\) | \(-1582861822122645504\) | \([2]\) | \(2359296\) | \(2.1783\) | |
| 228888.bz1 | 228888u4 | \([0, 0, 0, -1228539, -524050058]\) | \(5690357426/891\) | \(32109142898055168\) | \([2]\) | \(2359296\) | \(2.1783\) |
Rank
sage: E.rank()
The elliptic curves in class 228888u have rank \(0\).
Complex multiplication
The elliptic curves in class 228888u do not have complex multiplication.Modular form 228888.2.a.u
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.
