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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 450840bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.bo2 | 450840bo1 | \([0, 1, 0, 207984, -38547216]\) | \(40254822716/49359375\) | \(-1220009287536000000\) | \([2]\) | \(4976640\) | \(2.1566\) | \(\Gamma_0(N)\)-optimal* |
450840.bo1 | 450840bo2 | \([0, 1, 0, -1237016, -371475216]\) | \(4234737878642/1247410125\) | \(61664149429219584000\) | \([2]\) | \(9953280\) | \(2.5031\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450840bo have rank \(0\).
Complex multiplication
The elliptic curves in class 450840bo do not have complex multiplication.Modular form 450840.2.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 Cremona 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 Cremona labels.