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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 66654bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66654.bo2 | 66654bk1 | \([1, -1, 1, -34220, -48867425]\) | \(-3375/784\) | \(-1029423587521917168\) | \([2]\) | \(847872\) | \(2.1355\) | \(\Gamma_0(N)\)-optimal |
| 66654.bo1 | 66654bk2 | \([1, -1, 1, -2224280, -1264788737]\) | \(926859375/9604\) | \(12610438947143485308\) | \([2]\) | \(1695744\) | \(2.4821\) |
Rank
sage: E.rank()
The elliptic curves in class 66654bk have rank \(0\).
Complex multiplication
The elliptic curves in class 66654bk do not have complex multiplication.Modular form 66654.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
