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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 92736bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.ba2 | 92736bq1 | \([0, 0, 0, 192084, -74884304]\) | \(4101378352343/15049939968\) | \(-2876088316506144768\) | \([2]\) | \(1474560\) | \(2.2248\) | \(\Gamma_0(N)\)-optimal |
| 92736.ba1 | 92736bq2 | \([0, 0, 0, -1927596, -899863760]\) | \(4144806984356137/568114785504\) | \(108568426219416059904\) | \([2]\) | \(2949120\) | \(2.5714\) |
Rank
sage: E.rank()
The elliptic curves in class 92736bq have rank \(1\).
Complex multiplication
The elliptic curves in class 92736bq do not have complex multiplication.Modular form 92736.2.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.
