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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 291312bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 291312.bu2 | 291312bu1 | \([0, 0, 0, -895611, 457547690]\) | \(-1102302937/616896\) | \(-44462405874834210816\) | \([2]\) | \(5308416\) | \(2.4734\) | \(\Gamma_0(N)\)-optimal |
| 291312.bu1 | 291312bu2 | \([0, 0, 0, -15877371, 24347462186]\) | \(6141556990297/1019592\) | \(73486476376462098432\) | \([2]\) | \(10616832\) | \(2.8200\) |
Rank
sage: E.rank()
The elliptic curves in class 291312bu have rank \(0\).
Complex multiplication
The elliptic curves in class 291312bu do not have complex multiplication.Modular form 291312.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
