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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 338100bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338100.bi1 | 338100bi1 | \([0, -1, 0, -251533, 20081062]\) | \(174456832/83835\) | \(845761160711250000\) | \([2]\) | \(3870720\) | \(2.1337\) | \(\Gamma_0(N)\)-optimal |
| 338100.bi2 | 338100bi2 | \([0, -1, 0, 906092, 152050312]\) | \(509680208/357075\) | \(-57637056878100000000\) | \([2]\) | \(7741440\) | \(2.4802\) |
Rank
sage: E.rank()
The elliptic curves in class 338100bi have rank \(0\).
Complex multiplication
The elliptic curves in class 338100bi do not have complex multiplication.Modular form 338100.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
