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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 66654.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66654.bq1 | 66654bj2 | \([1, -1, 1, -2882885, 1764560445]\) | \(24553362849625/1755162752\) | \(189413940104032758912\) | \([2]\) | \(2838528\) | \(2.6378\) | |
| 66654.bq2 | 66654bj1 | \([1, -1, 1, 164155, 120377661]\) | \(4533086375/60669952\) | \(-6547389774052442112\) | \([2]\) | \(1419264\) | \(2.2912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66654.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 66654.bq do not have complex multiplication.Modular form 66654.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
