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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 101150.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.bu1 | 101150cs2 | \([1, 1, 1, -328888, -102146469]\) | \(-417267265/235298\) | \(-2218563168188281250\) | \([]\) | \(1814400\) | \(2.2235\) | |
101150.bu2 | 101150cs1 | \([1, 1, 1, 32362, 1893531]\) | \(397535/392\) | \(-3696065253125000\) | \([]\) | \(604800\) | \(1.6742\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101150.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 101150.bu do not have complex multiplication.Modular form 101150.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.