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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 450800.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.k1 | 450800k2 | \([0, 1, 0, -461008, -52350012]\) | \(5756278756/2705927\) | \(5093593689968000000\) | \([2]\) | \(7372800\) | \(2.2838\) | \(\Gamma_0(N)\)-optimal* |
450800.k2 | 450800k1 | \([0, 1, 0, 102492, -6143012]\) | \(253012016/181447\) | \(-85388232412000000\) | \([2]\) | \(3686400\) | \(1.9372\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800.k have rank \(0\).
Complex multiplication
The elliptic curves in class 450800.k do not have complex multiplication.Modular form 450800.2.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 LMFDB 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 LMFDB labels.