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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 126960.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.q1 | 126960ba4 | \([0, -1, 0, -934425776, 10994554397376]\) | \(148809678420065817601/20700\) | \(12551548527820800\) | \([4]\) | \(19464192\) | \(3.4139\) | |
| 126960.q2 | 126960ba6 | \([0, -1, 0, -218625296, -1065715442880]\) | \(1905890658841300321/293666194803750\) | \(178065965944915197066240000\) | \([2]\) | \(38928384\) | \(3.7605\) | |
| 126960.q3 | 126960ba3 | \([0, -1, 0, -59925296, 162368637120]\) | \(39248884582600321/3935264062500\) | \(2386167045906182400000000\) | \([2, 2]\) | \(19464192\) | \(3.4139\) | |
| 126960.q4 | 126960ba2 | \([0, -1, 0, -58401776, 171803491776]\) | \(36330796409313601/428490000\) | \(259817054525890560000\) | \([2, 2]\) | \(9732096\) | \(3.0673\) | |
| 126960.q5 | 126960ba1 | \([0, -1, 0, -3555056, 2831716800]\) | \(-8194759433281/965779200\) | \(-585605048114007244800\) | \([2]\) | \(4866048\) | \(2.7208\) | \(\Gamma_0(N)\)-optimal |
| 126960.q6 | 126960ba5 | \([0, -1, 0, 74398384, 786597642816]\) | \(75108181893694559/484313964843750\) | \(-293666194803750000000000000\) | \([2]\) | \(38928384\) | \(3.7605\) |
Rank
sage: E.rank()
The elliptic curves in class 126960.q have rank \(1\).
Complex multiplication
The elliptic curves in class 126960.q do not have complex multiplication.Modular form 126960.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
