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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 36162r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36162.o2 | 36162r1 | \([1, -1, 0, -8534535, 8835970877]\) | \(801581275315909089/70810888830976\) | \(6073175259595036164096\) | \([]\) | \(2370816\) | \(2.9200\) | \(\Gamma_0(N)\)-optimal |
| 36162.o1 | 36162r2 | \([1, -1, 0, -4238588895, -106212522853963]\) | \(98191033604529537629349729/10906239337336\) | \(935385842660919193656\) | \([]\) | \(16595712\) | \(3.8930\) |
Rank
sage: E.rank()
The elliptic curves in class 36162r have rank \(1\).
Complex multiplication
The elliptic curves in class 36162r do not have complex multiplication.Modular form 36162.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
