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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 154128bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154128.w3 | 154128bq1 | \([0, -1, 0, -21688, -86672]\) | \(57066625/32832\) | \(649108656488448\) | \([2]\) | \(622080\) | \(1.5318\) | \(\Gamma_0(N)\)-optimal |
| 154128.w4 | 154128bq2 | \([0, -1, 0, 86472, -778896]\) | \(3616805375/2105352\) | \(-41624092597321728\) | \([2]\) | \(1244160\) | \(1.8784\) | |
| 154128.w1 | 154128bq3 | \([0, -1, 0, -1157368, 479624560]\) | \(8671983378625/82308\) | \(1627279340224512\) | \([2]\) | \(1866240\) | \(2.0811\) | |
| 154128.w2 | 154128bq4 | \([0, -1, 0, -1130328, 503073648]\) | \(-8078253774625/846825858\) | \(-16742263491899891712\) | \([2]\) | \(3732480\) | \(2.4277\) |
Rank
sage: E.rank()
The elliptic curves in class 154128bq have rank \(1\).
Complex multiplication
The elliptic curves in class 154128bq do not have complex multiplication.Modular form 154128.2.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.
