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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 179088bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179088.u2 | 179088bk1 | \([0, -1, 0, 224952, 1372526064]\) | \(307348720697576375/198884536470802728\) | \(-814631061384407973888\) | \([]\) | \(5660928\) | \(2.6915\) | \(\Gamma_0(N)\)-optimal |
| 179088.u1 | 179088bk2 | \([0, -1, 0, -86730168, 310956267888]\) | \(-17614662728794756493037625/2607524922260224512\) | \(-10680422081577879601152\) | \([]\) | \(16982784\) | \(3.2408\) |
Rank
sage: E.rank()
The elliptic curves in class 179088bk have rank \(1\).
Complex multiplication
The elliptic curves in class 179088bk do not have complex multiplication.Modular form 179088.2.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.
