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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 121968.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121968.bs1 | 121968bs2 | \([0, 0, 0, -427251, -89222254]\) | \(2450086/441\) | \(1552495094234929152\) | \([2]\) | \(1351680\) | \(2.2096\) | |
121968.bs2 | 121968bs1 | \([0, 0, 0, 51909, -8052550]\) | \(8788/21\) | \(-36964168910355456\) | \([2]\) | \(675840\) | \(1.8630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121968.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 121968.bs do not have complex multiplication.Modular form 121968.2.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.