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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 388080db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.db3 | 388080db1 | \([0, 0, 0, -1436043, -661889158]\) | \(932288503609/779625\) | \(273880727898624000\) | \([2]\) | \(7077888\) | \(2.2739\) | \(\Gamma_0(N)\)-optimal |
| 388080.db2 | 388080db2 | \([0, 0, 0, -1753563, -347607862]\) | \(1697509118089/833765625\) | \(292900222891584000000\) | \([2, 2]\) | \(14155776\) | \(2.6204\) | |
| 388080.db1 | 388080db3 | \([0, 0, 0, -14983563, 22082534138]\) | \(1058993490188089/13182390375\) | \(4630947790731204096000\) | \([2]\) | \(28311552\) | \(2.9670\) | |
| 388080.db4 | 388080db4 | \([0, 0, 0, 6396117, -2663746918]\) | \(82375335041831/56396484375\) | \(-19811973951000000000000\) | \([2]\) | \(28311552\) | \(2.9670\) |
Rank
sage: E.rank()
The elliptic curves in class 388080db have rank \(0\).
Complex multiplication
The elliptic curves in class 388080db do not have complex multiplication.Modular form 388080.2.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 Cremona 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 Cremona labels.
