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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 173264.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173264.bk1 | 173264v2 | \([0, 0, 0, -9186667, 10717292250]\) | \(177930109857804849/634933\) | \(305968056389632\) | \([2]\) | \(5529600\) | \(2.4213\) | |
| 173264.bk2 | 173264v1 | \([0, 0, 0, -574427, 167298250]\) | \(43499078731809/82055753\) | \(39541871758118912\) | \([2]\) | \(2764800\) | \(2.0747\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 173264.bk have rank \(2\).
Complex multiplication
The elliptic curves in class 173264.bk do not have complex multiplication.Modular form 173264.2.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 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.
