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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 108900bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 108900.bs2 | 108900bq1 | \([0, 0, 0, -36300, 43091125]\) | \(-16384/2475\) | \(-799095805818750000\) | \([2]\) | \(1105920\) | \(2.1146\) | \(\Gamma_0(N)\)-optimal |
| 108900.bs1 | 108900bq2 | \([0, 0, 0, -2078175, 1143661750]\) | \(192143824/1815\) | \(9376057454940000000\) | \([2]\) | \(2211840\) | \(2.4611\) |
Rank
sage: E.rank()
The elliptic curves in class 108900bq have rank \(2\).
Complex multiplication
The elliptic curves in class 108900bq do not have complex multiplication.Modular form 108900.2.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.
