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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 110352bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110352.t2 | 110352bg1 | \([0, -1, 0, -703413, -244556739]\) | \(-5304438784000/497763387\) | \(-3611927362097590272\) | \([]\) | \(1555200\) | \(2.3030\) | \(\Gamma_0(N)\)-optimal |
| 110352.t1 | 110352bg2 | \([0, -1, 0, -58202613, -170888382531]\) | \(-3004935183806464000/2037123\) | \(-14782003851276288\) | \([]\) | \(4665600\) | \(2.8523\) |
Rank
sage: E.rank()
The elliptic curves in class 110352bg have rank \(0\).
Complex multiplication
The elliptic curves in class 110352bg do not have complex multiplication.Modular form 110352.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
