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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 11088.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.bq1 | 11088by2 | \([0, 0, 0, -7419, 227050]\) | \(15124197817/1294139\) | \(3864278347776\) | \([2]\) | \(18432\) | \(1.1564\) | |
| 11088.bq2 | 11088by1 | \([0, 0, 0, 501, 16378]\) | \(4657463/41503\) | \(-123927293952\) | \([2]\) | \(9216\) | \(0.80986\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.bq do not have complex multiplication.Modular form 11088.2.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 LMFDB 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 LMFDB labels.
