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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 230640.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.db1 | 230640db3 | \([0, 1, 0, -6381360, 6202188468]\) | \(15811147933922/1016955\) | \(1848425074506455040\) | \([4]\) | \(5898240\) | \(2.5626\) | |
| 230640.db2 | 230640db4 | \([0, 1, 0, -2152960, -1142465452]\) | \(607199886722/41558445\) | \(75536942928150620160\) | \([2]\) | \(5898240\) | \(2.5626\) | |
| 230640.db3 | 230640db2 | \([0, 1, 0, -423160, 84308708]\) | \(9220796644/1946025\) | \(1768554855237657600\) | \([2, 2]\) | \(2949120\) | \(2.2160\) | |
| 230640.db4 | 230640db1 | \([0, 1, 0, 57340, 8005308]\) | \(91765424/174375\) | \(-39618164319840000\) | \([2]\) | \(1474560\) | \(1.8695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230640.db have rank \(0\).
Complex multiplication
The elliptic curves in class 230640.db do not have complex multiplication.Modular form 230640.2.a.db
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.
