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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 160080bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.c2 | 160080bq1 | \([0, -1, 0, 824, -3344]\) | \(15087533111/9724860\) | \(-39833026560\) | \([2]\) | \(129024\) | \(0.72292\) | \(\Gamma_0(N)\)-optimal |
| 160080.c1 | 160080bq2 | \([0, -1, 0, -3496, -24080]\) | \(1153990560169/600600150\) | \(2460058214400\) | \([2]\) | \(258048\) | \(1.0695\) |
Rank
sage: E.rank()
The elliptic curves in class 160080bq have rank \(2\).
Complex multiplication
The elliptic curves in class 160080bq do not have complex multiplication.Modular form 160080.2.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 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.
