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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 78400.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.bo1 | 78400n2 | \([0, 1, 0, -785633, -268299137]\) | \(-5452947409/250\) | \(-2458624000000000\) | \([]\) | \(829440\) | \(2.0288\) | |
78400.bo2 | 78400n1 | \([0, 1, 0, -1633, -955137]\) | \(-49/40\) | \(-393379840000000\) | \([]\) | \(276480\) | \(1.4795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 78400.bo do not have complex multiplication.Modular form 78400.2.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.