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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 120666.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120666.o1 | 120666d6 | \([1, 1, 0, -2318444079, -42968757113667]\) | \(285531136548675601769470657/17941034271597192\) | \(86597945691453770720328\) | \([2]\) | \(70778880\) | \(3.8616\) | |
| 120666.o2 | 120666d4 | \([1, 1, 0, -145178439, -668749349835]\) | \(70108386184777836280897/552468975892674624\) | \(2666662225059544909194816\) | \([2, 2]\) | \(35389440\) | \(3.5150\) | |
| 120666.o3 | 120666d5 | \([1, 1, 0, -49450079, -1537369342803]\) | \(-2770540998624539614657/209924951154647363208\) | \(-1013267643557812284558643272\) | \([2]\) | \(70778880\) | \(3.8616\) | |
| 120666.o4 | 120666d2 | \([1, 1, 0, -15332359, 5801035765]\) | \(82582985847542515777/44772582831427584\) | \(216108705763980145299456\) | \([2, 2]\) | \(17694720\) | \(3.1685\) | |
| 120666.o5 | 120666d1 | \([1, 1, 0, -11871239, 15718529013]\) | \(38331145780597164097/55468445663232\) | \(267735592743299186688\) | \([2]\) | \(8847360\) | \(2.8219\) | \(\Gamma_0(N)\)-optimal |
| 120666.o6 | 120666d3 | \([1, 1, 0, 59135801, 45701075893]\) | \(4738217997934888496063/2928751705237796928\) | \(-14136525089607145352242752\) | \([2]\) | \(35389440\) | \(3.5150\) |
Rank
sage: E.rank()
The elliptic curves in class 120666.o have rank \(0\).
Complex multiplication
The elliptic curves in class 120666.o do not have complex multiplication.Modular form 120666.2.a.o
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.
