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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 337896.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 337896.bq1 | 337896bq4 | \([0, 0, 0, -988779, -369165098]\) | \(3044193988/85293\) | \(2995452800213971968\) | \([2]\) | \(6193152\) | \(2.3244\) | |
| 337896.bq2 | 337896bq2 | \([0, 0, 0, -144039, 12826330]\) | \(37642192/13689\) | \(120187920996239616\) | \([2, 2]\) | \(3096576\) | \(1.9778\) | |
| 337896.bq3 | 337896bq1 | \([0, 0, 0, -127794, 17579617]\) | \(420616192/117\) | \(64202949250128\) | \([2]\) | \(1548288\) | \(1.6312\) | \(\Gamma_0(N)\)-optimal |
| 337896.bq4 | 337896bq3 | \([0, 0, 0, 440781, 90607390]\) | \(269676572/257049\) | \(-9027448288161997824\) | \([2]\) | \(6193152\) | \(2.3244\) |
Rank
sage: E.rank()
The elliptic curves in class 337896.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 337896.bq do not have complex multiplication.Modular form 337896.2.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.
