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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 32799i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32799.d4 | 32799i1 | \([1, 0, 0, 403, -6600]\) | \(12167/39\) | \(-23198109519\) | \([2]\) | \(22400\) | \(0.67213\) | \(\Gamma_0(N)\)-optimal |
32799.d3 | 32799i2 | \([1, 0, 0, -3802, -78085]\) | \(10218313/1521\) | \(904726271241\) | \([2, 2]\) | \(44800\) | \(1.0187\) | |
32799.d2 | 32799i3 | \([1, 0, 0, -16417, 731798]\) | \(822656953/85683\) | \(50966246613243\) | \([2]\) | \(89600\) | \(1.3653\) | |
32799.d1 | 32799i4 | \([1, 0, 0, -58467, -5446188]\) | \(37159393753/1053\) | \(626348957013\) | \([2]\) | \(89600\) | \(1.3653\) |
Rank
sage: E.rank()
The elliptic curves in class 32799i have rank \(1\).
Complex multiplication
The elliptic curves in class 32799i do not have complex multiplication.Modular form 32799.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.