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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 41400.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41400.bs1 | 41400bd2 | \([0, 0, 0, -303075, -62147250]\) | \(9776035692/359375\) | \(113177250000000000\) | \([2]\) | \(331776\) | \(2.0417\) | |
41400.bs2 | 41400bd1 | \([0, 0, 0, 7425, -3462750]\) | \(574992/66125\) | \(-5206153500000000\) | \([2]\) | \(165888\) | \(1.6951\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41400.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 41400.bs do not have complex multiplication.Modular form 41400.2.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.