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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 87120.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.bk1 | 87120ec4 | \([0, 0, 0, -1031283, -402997518]\) | \(22930509321/6875\) | \(36367738007040000\) | \([2]\) | \(983040\) | \(2.1557\) | |
| 87120.bk2 | 87120ec3 | \([0, 0, 0, -508563, 136344978]\) | \(2749884201/73205\) | \(387243674298961920\) | \([2]\) | \(983040\) | \(2.1557\) | |
| 87120.bk3 | 87120ec2 | \([0, 0, 0, -72963, -4528062]\) | \(8120601/3025\) | \(16001804723097600\) | \([2, 2]\) | \(491520\) | \(1.8092\) | |
| 87120.bk4 | 87120ec1 | \([0, 0, 0, 14157, -503118]\) | \(59319/55\) | \(-290941904056320\) | \([2]\) | \(245760\) | \(1.4626\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 87120.bk do not have complex multiplication.Modular form 87120.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
