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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 14490bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.bm2 | 14490bq1 | \([1, -1, 1, -14513, -669283]\) | \(463702796512201/15214500\) | \(11091370500\) | \([2]\) | \(23040\) | \(1.0212\) | \(\Gamma_0(N)\)-optimal |
| 14490.bm3 | 14490bq2 | \([1, -1, 1, -13883, -730519]\) | \(-405897921250921/84358968750\) | \(-61497688218750\) | \([2]\) | \(46080\) | \(1.3677\) | |
| 14490.bm1 | 14490bq3 | \([1, -1, 1, -25988, 536807]\) | \(2662558086295801/1374177967680\) | \(1001775738438720\) | \([6]\) | \(69120\) | \(1.5705\) | |
| 14490.bm4 | 14490bq4 | \([1, -1, 1, 97492, 4093031]\) | \(140574743422291079/91397357868600\) | \(-66628673886209400\) | \([6]\) | \(138240\) | \(1.9170\) |
Rank
sage: E.rank()
The elliptic curves in class 14490bq have rank \(1\).
Complex multiplication
The elliptic curves in class 14490bq do not have complex multiplication.Modular form 14490.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
