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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 202800.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.bs1 | 202800fe2 | \([0, -1, 0, -3111008, 1893040512]\) | \(10779215329/1232010\) | \(380587325189760000000\) | \([2]\) | \(9289728\) | \(2.6813\) | |
| 202800.bs2 | 202800fe1 | \([0, -1, 0, 268992, 148960512]\) | \(6967871/35100\) | \(-10842943737600000000\) | \([2]\) | \(4644864\) | \(2.3347\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.bs have rank \(2\).
Complex multiplication
The elliptic curves in class 202800.bs do not have complex multiplication.Modular form 202800.2.a.bs
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.
