Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 139656ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139656.e3 | 139656ba1 | \([0, -1, 0, -6524, 197748]\) | \(810448/33\) | \(1250607190272\) | \([2]\) | \(197120\) | \(1.0870\) | \(\Gamma_0(N)\)-optimal |
| 139656.e2 | 139656ba2 | \([0, -1, 0, -17104, -593636]\) | \(3650692/1089\) | \(165080149115904\) | \([2, 2]\) | \(394240\) | \(1.4336\) | |
| 139656.e4 | 139656ba3 | \([0, -1, 0, 46376, -4021556]\) | \(36382894/43923\) | \(-13316465362016256\) | \([2]\) | \(788480\) | \(1.7802\) | |
| 139656.e1 | 139656ba4 | \([0, -1, 0, -249864, -47983572]\) | \(5690357426/891\) | \(270131153098752\) | \([2]\) | \(788480\) | \(1.7802\) |
Rank
sage: E.rank()
The elliptic curves in class 139656ba have rank \(0\).
Complex multiplication
The elliptic curves in class 139656ba do not have complex multiplication.Modular form 139656.2.a.ba
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.
