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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 99372bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99372.bb2 | 99372bu1 | \([0, 1, 0, -44165, -3224376]\) | \(1048576/117\) | \(1063051239820752\) | \([2]\) | \(725760\) | \(1.6163\) | \(\Gamma_0(N)\)-optimal |
| 99372.bb1 | 99372bu2 | \([0, 1, 0, -168380, 23109204]\) | \(3631696/507\) | \(73704885960905472\) | \([2]\) | \(1451520\) | \(1.9629\) |
Rank
sage: E.rank()
The elliptic curves in class 99372bu have rank \(0\).
Complex multiplication
The elliptic curves in class 99372bu do not have complex multiplication.Modular form 99372.2.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.
