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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 47610o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.j2 | 47610o1 | \([1, -1, 0, -599985, -237793559]\) | \(-18191447/8100\) | \(-10635626350672868700\) | \([2]\) | \(1413120\) | \(2.3578\) | \(\Gamma_0(N)\)-optimal |
47610.j1 | 47610o2 | \([1, -1, 0, -10455255, -13008252425]\) | \(96260823287/11250\) | \(14771703264823428750\) | \([2]\) | \(2826240\) | \(2.7044\) |
Rank
sage: E.rank()
The elliptic curves in class 47610o have rank \(1\).
Complex multiplication
The elliptic curves in class 47610o do not have complex multiplication.Modular form 47610.2.a.o
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.