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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 378560bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 378560.bk2 | 378560bk1 | \([0, 1, 0, -12384545, -13637949857]\) | \(166021325905681/32614400000\) | \(41267620596835942400000\) | \([2]\) | \(36126720\) | \(3.0561\) | \(\Gamma_0(N)\)-optimal |
| 378560.bk1 | 378560bk2 | \([0, 1, 0, -60840225, 170367649375]\) | \(19683218700810001/1478750000000\) | \(1871090498600960000000000\) | \([2]\) | \(72253440\) | \(3.4027\) |
Rank
sage: E.rank()
The elliptic curves in class 378560bk have rank \(1\).
Complex multiplication
The elliptic curves in class 378560bk do not have complex multiplication.Modular form 378560.2.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.
