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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 64680.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64680.db1 | 64680bc4 | \([0, 1, 0, -798440120, 7690851577968]\) | \(233632133015204766393938/29145526885986328125\) | \(7022473405664062500000000000\) | \([2]\) | \(47185920\) | \(4.0729\) | |
| 64680.db2 | 64680bc2 | \([0, 1, 0, -199438640, -959688195600]\) | \(7282213870869695463556/912102595400390625\) | \(109883349244170810000000000\) | \([2, 2]\) | \(23592960\) | \(3.7263\) | |
| 64680.db3 | 64680bc1 | \([0, 1, 0, -193008860, -1032128668992]\) | \(26401417552259125806544/507547744790625\) | \(15286396064479293600000\) | \([2]\) | \(11796480\) | \(3.3797\) | \(\Gamma_0(N)\)-optimal |
| 64680.db4 | 64680bc3 | \([0, 1, 0, 296686360, -4973934795600]\) | \(11986661998777424518222/51295853620928503125\) | \(-12359487247664368566585600000\) | \([2]\) | \(47185920\) | \(4.0729\) |
Rank
sage: E.rank()
The elliptic curves in class 64680.db have rank \(0\).
Complex multiplication
The elliptic curves in class 64680.db do not have complex multiplication.Modular form 64680.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
