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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 70560bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.df3 | 70560bi1 | \([0, 0, 0, -13377, 573496]\) | \(48228544/2025\) | \(11115289281600\) | \([2, 2]\) | \(147456\) | \(1.2680\) | \(\Gamma_0(N)\)-optimal |
| 70560.df4 | 70560bi2 | \([0, 0, 0, 6468, 2129344]\) | \(85184/5625\) | \(-1976051427840000\) | \([2]\) | \(294912\) | \(1.6146\) | |
| 70560.df2 | 70560bi3 | \([0, 0, 0, -35427, -1803494]\) | \(111980168/32805\) | \(1440541490895360\) | \([2]\) | \(294912\) | \(1.6146\) | |
| 70560.df1 | 70560bi4 | \([0, 0, 0, -211827, 37524886]\) | \(23937672968/45\) | \(1976051427840\) | \([2]\) | \(294912\) | \(1.6146\) |
Rank
sage: E.rank()
The elliptic curves in class 70560bi have rank \(0\).
Complex multiplication
The elliptic curves in class 70560bi do not have complex multiplication.Modular form 70560.2.a.bi
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
