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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 66924o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66924.c2 | 66924o1 | \([0, 0, 0, -166296, -1076782655]\) | \(-9033613312/8891539371\) | \(-500592778998273829296\) | \([2]\) | \(1806336\) | \(2.6509\) | \(\Gamma_0(N)\)-optimal |
66924.c1 | 66924o2 | \([0, 0, 0, -16798431, -26201285786]\) | \(581972233018192/7558011747\) | \(6808244910162165879552\) | \([2]\) | \(3612672\) | \(2.9975\) |
Rank
sage: E.rank()
The elliptic curves in class 66924o have rank \(0\).
Complex multiplication
The elliptic curves in class 66924o do not have complex multiplication.Modular form 66924.2.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.