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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 33462bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.f1 | 33462bk1 | \([1, -1, 0, -44901, -4895019]\) | \(-16835377/7744\) | \(-4605106634796096\) | \([]\) | \(239616\) | \(1.7119\) | \(\Gamma_0(N)\)-optimal |
| 33462.f2 | 33462bk2 | \([1, -1, 0, 350559, 57983121]\) | \(8011835663/7086244\) | \(-4213960390003102596\) | \([3]\) | \(718848\) | \(2.2612\) |
Rank
sage: E.rank()
The elliptic curves in class 33462bk have rank \(1\).
Complex multiplication
The elliptic curves in class 33462bk do not have complex multiplication.Modular form 33462.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
