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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 116886.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116886.bo1 | 116886bm1 | \([1, 0, 0, -1016463, -394529607]\) | \(-65560514292015625/149954112\) | \(-265652856608832\) | \([]\) | \(1762560\) | \(2.0116\) | \(\Gamma_0(N)\)-optimal |
116886.bo2 | 116886bm2 | \([1, 0, 0, -698838, -645156060]\) | \(-21305767155765625/89149883547648\) | \(-157934456847554838528\) | \([]\) | \(5287680\) | \(2.5609\) |
Rank
sage: E.rank()
The elliptic curves in class 116886.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 116886.bo do not have complex multiplication.Modular form 116886.2.a.bo
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.