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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 183872.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
183872.bo1 | 183872bz2 | \([0, 0, 0, -126738508, 549175302000]\) | \(177930109857804849/634933\) | \(803392800370720768\) | \([2]\) | \(20643840\) | \(3.0774\) | |
183872.bo2 | 183872bz1 | \([0, 0, 0, -7924748, 8572694000]\) | \(43499078731809/82055753\) | \(103826704847910207488\) | \([2]\) | \(10321920\) | \(2.7308\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 183872.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 183872.bo do not have complex multiplication.Modular form 183872.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.