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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 159936.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.cq1 | 159936jf2 | \([0, -1, 0, -7677973, -8186230835]\) | \(-1272481306550272000/5865429267\) | \(-230734162658377728\) | \([]\) | \(3525120\) | \(2.5350\) | |
| 159936.cq2 | 159936jf1 | \([0, -1, 0, -57493, -20124467]\) | \(-534274048000/4146834123\) | \(-163128094381228032\) | \([]\) | \(1175040\) | \(1.9857\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159936.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 159936.cq do not have complex multiplication.Modular form 159936.2.a.cq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
