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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 112710.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112710.bq1 | 112710bl4 | \([1, 0, 1, -404173, -95421322]\) | \(302503589987689/12214946250\) | \(294839107940666250\) | \([2]\) | \(2359296\) | \(2.1182\) | |
| 112710.bq2 | 112710bl2 | \([1, 0, 1, -66043, 4529906]\) | \(1319778683209/395612100\) | \(9549114360984900\) | \([2, 2]\) | \(1179648\) | \(1.7716\) | |
| 112710.bq3 | 112710bl1 | \([1, 0, 1, -60263, 5688218]\) | \(1002702430729/159120\) | \(3840769979280\) | \([2]\) | \(589824\) | \(1.4250\) | \(\Gamma_0(N)\)-optimal |
| 112710.bq4 | 112710bl3 | \([1, 0, 1, 179607, 30372286]\) | \(26546265663191/31856082570\) | \(-768928391103072330\) | \([2]\) | \(2359296\) | \(2.1182\) |
Rank
sage: E.rank()
The elliptic curves in class 112710.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 112710.bq do not have complex multiplication.Modular form 112710.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
