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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 126960bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.bl2 | 126960bq1 | \([0, -1, 0, 1134000, -479400000]\) | \(265971760991/317400000\) | \(-192457077426585600000\) | \([2]\) | \(3041280\) | \(2.5784\) | \(\Gamma_0(N)\)-optimal |
| 126960.bl1 | 126960bq2 | \([0, -1, 0, -6652880, -4572184128]\) | \(53706380371489/16171875000\) | \(9805897287360000000000\) | \([2]\) | \(6082560\) | \(2.9250\) |
Rank
sage: E.rank()
The elliptic curves in class 126960bq have rank \(0\).
Complex multiplication
The elliptic curves in class 126960bq do not have complex multiplication.Modular form 126960.2.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.
