Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 159600.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159600.bq1 | 159600gz3 | \([0, -1, 0, -80808, 7364112]\) | \(1823652903746/328593657\) | \(10514997024000000\) | \([2]\) | \(1310720\) | \(1.7933\) | |
| 159600.bq2 | 159600gz2 | \([0, -1, 0, -23808, -1299888]\) | \(93280467172/7800849\) | \(124813584000000\) | \([2, 2]\) | \(655360\) | \(1.4467\) | |
| 159600.bq3 | 159600gz1 | \([0, -1, 0, -23308, -1361888]\) | \(350104249168/2793\) | \(11172000000\) | \([2]\) | \(327680\) | \(1.1002\) | \(\Gamma_0(N)\)-optimal |
| 159600.bq4 | 159600gz4 | \([0, -1, 0, 25192, -6003888]\) | \(55251546334/517244049\) | \(-16551809568000000\) | \([2]\) | \(1310720\) | \(1.7933\) |
Rank
sage: E.rank()
The elliptic curves in class 159600.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 159600.bq do not have complex multiplication.Modular form 159600.2.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.
