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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 177600.ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177600.ey1 | 177600fo4 | \([0, 1, 0, -512733633, -920165335137]\) | \(3639478711331685826729/2016912141902025000\) | \(8261272133230694400000000000\) | \([2]\) | \(106168320\) | \(4.0472\) | |
| 177600.ey2 | 177600fo2 | \([0, 1, 0, -312733633, 2116034664863]\) | \(825824067562227826729/5613755625000000\) | \(22993943040000000000000000\) | \([2, 2]\) | \(53084160\) | \(3.7007\) | |
| 177600.ey3 | 177600fo1 | \([0, 1, 0, -312221633, 2123348584863]\) | \(821774646379511057449/38361600000\) | \(157129113600000000000\) | \([2]\) | \(26542080\) | \(3.3541\) | \(\Gamma_0(N)\)-optimal |
| 177600.ey4 | 177600fo3 | \([0, 1, 0, -120925633, 4684151976863]\) | \(-47744008200656797609/2286529541015625000\) | \(-9365625000000000000000000000\) | \([2]\) | \(106168320\) | \(4.0472\) |
Rank
sage: E.rank()
The elliptic curves in class 177600.ey have rank \(0\).
Complex multiplication
The elliptic curves in class 177600.ey do not have complex multiplication.Modular form 177600.2.a.ey
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.
