Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 38640.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.g1 | 38640bd4 | \([0, -1, 0, -48234536, -337641360]\) | \(3029968325354577848895529/1753440696000000000000\) | \(7182093090816000000000000\) | \([2]\) | \(6635520\) | \(3.4589\) | |
| 38640.g2 | 38640bd2 | \([0, -1, 0, -33181496, -73557058704]\) | \(986396822567235411402169/6336721794060000\) | \(25955212468469760000\) | \([2]\) | \(2211840\) | \(2.9096\) | |
| 38640.g3 | 38640bd1 | \([0, -1, 0, -2033976, -1195140240]\) | \(-227196402372228188089/19338934824115200\) | \(-79212277039575859200\) | \([2]\) | \(1105920\) | \(2.5631\) | \(\Gamma_0(N)\)-optimal |
| 38640.g4 | 38640bd3 | \([0, -1, 0, 12058584, -48234384]\) | \(47342661265381757089751/27397579603968000000\) | \(-112220486057852928000000\) | \([2]\) | \(3317760\) | \(3.1124\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.g have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.g do not have complex multiplication.Modular form 38640.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
