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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 98736bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.f1 | 98736bq1 | \([0, -1, 0, -728944, -29092160]\) | \(4435194707/2528172\) | \(24417473863069089792\) | \([2]\) | \(2838528\) | \(2.4100\) | \(\Gamma_0(N)\)-optimal |
| 98736.f2 | 98736bq2 | \([0, -1, 0, 2891376, -234726336]\) | \(276785390413/162620946\) | \(-1570618098192120569856\) | \([2]\) | \(5677056\) | \(2.7565\) |
Rank
sage: E.rank()
The elliptic curves in class 98736bq have rank \(1\).
Complex multiplication
The elliptic curves in class 98736bq do not have complex multiplication.Modular form 98736.2.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.
