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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 25200.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.bs1 | 25200dc2 | \([0, 0, 0, -8185875, -9014568750]\) | \(280844088456303/614656\) | \(132765696000000000\) | \([2]\) | \(737280\) | \(2.5320\) | |
25200.bs2 | 25200dc1 | \([0, 0, 0, -505875, -144168750]\) | \(-66282611823/3211264\) | \(-693633024000000000\) | \([2]\) | \(368640\) | \(2.1854\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.bs do not have complex multiplication.Modular form 25200.2.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.