Show commands for:
SageMath
sage: E = EllipticCurve("bq1")
sage: E.isogeny_class()
Elliptic curves in class 88935.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 88935.bq1 | 88935m6 | [1, 1, 0, -18078706923, -935626807637892] | [2] | 44236800 | |
| 88935.bq2 | 88935m4 | [1, 1, 0, -1129919298, -14619518822817] | [2, 2] | 22118400 | |
| 88935.bq3 | 88935m5 | [1, 1, 0, -1124316393, -14771672431578] | [2] | 44236800 | |
| 88935.bq4 | 88935m3 | [1, 1, 0, -150863528, 376052042997] | [2] | 22118400 | |
| 88935.bq5 | 88935m2 | [1, 1, 0, -70970253, -226071613368] | [2, 2] | 11059200 | |
| 88935.bq6 | 88935m1 | [1, 1, 0, 207392, -10559939837] | [2] | 5529600 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88935.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.bq do not have complex multiplication.Modular form 88935.2.a.bq
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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
