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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 281775.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
281775.bo1 | 281775bo1 | \([1, 1, 0, -4681525, -3900389000]\) | \(147815204204011553/15178486401\) | \(1165185995126765625\) | \([2]\) | \(6389760\) | \(2.4995\) | \(\Gamma_0(N)\)-optimal |
281775.bo2 | 281775bo2 | \([1, 1, 0, -4322400, -4523470875]\) | \(-116340772335201233/47730591665289\) | \(-3664068700805700890625\) | \([2]\) | \(12779520\) | \(2.8461\) |
Rank
sage: E.rank()
The elliptic curves in class 281775.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 281775.bo do not have complex multiplication.Modular form 281775.2.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.