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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 259182.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.eb1 | 259182eb4 | \([1, -1, 1, -37017311, -86676305295]\) | \(4343648411957162113/100157326038\) | \(129349978438766676822\) | \([2]\) | \(21626880\) | \(2.9721\) | |
| 259182.eb2 | 259182eb3 | \([1, -1, 1, -9944771, 10810042521]\) | \(84221775551938753/9668399813226\) | \(12486428670266961557994\) | \([2]\) | \(21626880\) | \(2.9721\) | |
| 259182.eb3 | 259182eb2 | \([1, -1, 1, -2398001, -1249695939]\) | \(1180831643443873/160443506916\) | \(207207650016043973604\) | \([2, 2]\) | \(10813440\) | \(2.6255\) | |
| 259182.eb4 | 259182eb1 | \([1, -1, 1, 237379, -103832715]\) | \(1145430322847/4265098992\) | \(-5508238732782187248\) | \([2]\) | \(5406720\) | \(2.2789\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.eb do not have complex multiplication.Modular form 259182.2.a.eb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
