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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 102850bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102850.h2 | 102850bo1 | \([1, 0, 1, -183076, 30135048]\) | \(118654379305/578\) | \(3305663281250\) | \([3]\) | \(552960\) | \(1.6024\) | \(\Gamma_0(N)\)-optimal |
102850.h1 | 102850bo2 | \([1, 0, 1, -258701, 2910048]\) | \(334799534905/193100552\) | \(1104369211653125000\) | \([]\) | \(1658880\) | \(2.1517\) |
Rank
sage: E.rank()
The elliptic curves in class 102850bo have rank \(1\).
Complex multiplication
The elliptic curves in class 102850bo do not have complex multiplication.Modular form 102850.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.