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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 162450.dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.dq1 | 162450be2 | \([1, -1, 1, -54625505, -92946451003]\) | \(4904335099/1822500\) | \(6698807531069122617187500\) | \([2]\) | \(28016640\) | \(3.4636\) | |
| 162450.dq2 | 162450be1 | \([1, -1, 1, -23760005, 43540789997]\) | \(403583419/10800\) | \(39696637221150356250000\) | \([2]\) | \(14008320\) | \(3.1170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162450.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 162450.dq do not have complex multiplication.Modular form 162450.2.a.dq
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
