Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 122550.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122550.o1 | 122550d4 | \([1, 1, 0, -724837171525, -237525013403901875]\) | \(2695411376533589106170675619466398289/2123546400000000\) | \(33180412500000000000\) | \([2]\) | \(739639296\) | \(4.9344\) | |
| 122550.o2 | 122550d2 | \([1, 1, 0, -45302323525, -3711342438909875]\) | \(658059431397928037221595991689809/18470704385855324160000\) | \(288604756028989440000000000\) | \([2, 2]\) | \(369819648\) | \(4.5879\) | |
| 122550.o3 | 122550d3 | \([1, 1, 0, -45244723525, -3721250618109875]\) | \(-655552536799502322424300617353809/3486819805571317382996428800\) | \(-54481559462051834109319200000000\) | \([2]\) | \(739639296\) | \(4.9344\) | |
| 122550.o4 | 122550d1 | \([1, 1, 0, -2834995525, -57835743741875]\) | \(161272686097343726562556430929/851057913027019721932800\) | \(13297779891047183155200000000\) | \([2]\) | \(184909824\) | \(4.2413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 122550.o have rank \(0\).
Complex multiplication
The elliptic curves in class 122550.o do not have complex multiplication.Modular form 122550.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
