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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 124950.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124950.cb1 | 124950ba6 | \([1, 1, 0, -16805289925, 838520099849125]\) | \(285531136548675601769470657/17941034271597192\) | \(32980386578424031900125000\) | \([2]\) | \(188743680\) | \(4.3568\) | |
| 124950.cb2 | 124950ba4 | \([1, 1, 0, -1052328925, 13049190488125]\) | \(70108386184777836280897/552468975892674624\) | \(1015584727262457450609000000\) | \([2, 2]\) | \(94371840\) | \(4.0102\) | |
| 124950.cb3 | 124950ba5 | \([1, 1, 0, -358439925, 30001592647125]\) | \(-2770540998624539614657/209924951154647363208\) | \(-385897821537392306782156125000\) | \([2]\) | \(188743680\) | \(4.3568\) | |
| 124950.cb4 | 124950ba2 | \([1, 1, 0, -111136925, -113379631875]\) | \(82582985847542515777/44772582831427584\) | \(82303899961478497344000000\) | \([2, 2]\) | \(47185920\) | \(3.6637\) | |
| 124950.cb5 | 124950ba1 | \([1, 1, 0, -86048925, -306883375875]\) | \(38331145780597164097/55468445663232\) | \(101965736934899712000000\) | \([2]\) | \(23592960\) | \(3.3171\) | \(\Gamma_0(N)\)-optimal |
| 124950.cb6 | 124950ba3 | \([1, 1, 0, 428647075, -891208375875]\) | \(4738217997934888496063/2928751705237796928\) | \(-5383823583898774543473000000\) | \([2]\) | \(94371840\) | \(4.0102\) |
Rank
sage: E.rank()
The elliptic curves in class 124950.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 124950.cb do not have complex multiplication.Modular form 124950.2.a.cb
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
