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SageMath
E = EllipticCurve("ny1")
E.isogeny_class()
Elliptic curves in class 242550ny
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.ny4 | 242550ny1 | \([1, -1, 1, -106805, -13316803]\) | \(2714704875/21296\) | \(1056988028250000\) | \([2]\) | \(1658880\) | \(1.7112\) | \(\Gamma_0(N)\)-optimal |
| 242550.ny3 | 242550ny2 | \([1, -1, 1, -180305, 7410197]\) | \(13060888875/7086244\) | \(351712766400187500\) | \([2]\) | \(3317760\) | \(2.0577\) | |
| 242550.ny2 | 242550ny3 | \([1, -1, 1, -713180, 223708447]\) | \(1108717875/45056\) | \(1630242427968000000\) | \([2]\) | \(4976640\) | \(2.2605\) | |
| 242550.ny1 | 242550ny4 | \([1, -1, 1, -11297180, 14617948447]\) | \(4406910829875/7744\) | \(280197917307000000\) | \([2]\) | \(9953280\) | \(2.6070\) |
Rank
sage: E.rank()
The elliptic curves in class 242550ny have rank \(0\).
Complex multiplication
The elliptic curves in class 242550ny do not have complex multiplication.Modular form 242550.2.a.ny
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
