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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 200400.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200400.bs1 | 200400m2 | \([0, 1, 0, -49808, 4250388]\) | \(213525509833/669336\) | \(42837504000000\) | \([2]\) | \(884736\) | \(1.4830\) | |
| 200400.bs2 | 200400m1 | \([0, 1, 0, -1808, 122388]\) | \(-10218313/96192\) | \(-6156288000000\) | \([2]\) | \(442368\) | \(1.1364\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 200400.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 200400.bs do not have complex multiplication.Modular form 200400.2.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.
