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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 17850.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17850.t1 | 17850o5 | \([1, 0, 1, -342965101, -2444714009152]\) | \(285531136548675601769470657/17941034271597192\) | \(280328660493706125000\) | \([2]\) | \(3932160\) | \(3.3838\) | |
| 17850.t2 | 17850o3 | \([1, 0, 1, -21476101, -38047355152]\) | \(70108386184777836280897/552468975892674624\) | \(8632327748323041000000\) | \([2, 2]\) | \(1966080\) | \(3.0373\) | |
| 17850.t3 | 17850o6 | \([1, 0, 1, -7315101, -87469245152]\) | \(-2770540998624539614657/209924951154647363208\) | \(-3280077361791365050125000\) | \([2]\) | \(3932160\) | \(3.3838\) | |
| 17850.t4 | 17850o2 | \([1, 0, 1, -2268101, 330228848]\) | \(82582985847542515777/44772582831427584\) | \(699571606741056000000\) | \([2, 2]\) | \(983040\) | \(2.6907\) | |
| 17850.t5 | 17850o1 | \([1, 0, 1, -1756101, 894452848]\) | \(38331145780597164097/55468445663232\) | \(866694463488000000\) | \([2]\) | \(491520\) | \(2.3441\) | \(\Gamma_0(N)\)-optimal |
| 17850.t6 | 17850o4 | \([1, 0, 1, 8747899, 2599524848]\) | \(4738217997934888496063/2928751705237796928\) | \(-45761745394340577000000\) | \([2]\) | \(1966080\) | \(3.0373\) |
Rank
sage: E.rank()
The elliptic curves in class 17850.t have rank \(0\).
Complex multiplication
The elliptic curves in class 17850.t do not have complex multiplication.Modular form 17850.2.a.t
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.
