Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 190608bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190608.w1 | 190608bu1 | \([0, -1, 0, -104360888, -410315521680]\) | \(-235484681972809299625/3345408\) | \(-1785761447804928\) | \([]\) | \(10886400\) | \(2.9336\) | \(\Gamma_0(N)\)-optimal |
| 190608.w2 | 190608bu2 | \([0, -1, 0, -103754408, -415320679824]\) | \(-231403026519578265625/5706597418401792\) | \(-3046152118941859574710272\) | \([]\) | \(32659200\) | \(3.4829\) |
Rank
sage: E.rank()
The elliptic curves in class 190608bu have rank \(1\).
Complex multiplication
The elliptic curves in class 190608bu do not have complex multiplication.Modular form 190608.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
