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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3366k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3366.i1 | 3366k1 | \([1, -1, 0, -8136, -278208]\) | \(81706955619457/744505344\) | \(542744395776\) | \([2]\) | \(8960\) | \(1.0739\) | \(\Gamma_0(N)\)-optimal |
3366.i2 | 3366k2 | \([1, -1, 0, -2376, -668736]\) | \(-2035346265217/264305213568\) | \(-192678500691072\) | \([2]\) | \(17920\) | \(1.4204\) |
Rank
sage: E.rank()
The elliptic curves in class 3366k have rank \(0\).
Complex multiplication
The elliptic curves in class 3366k do not have complex multiplication.Modular form 3366.2.a.k
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.