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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 187200.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.k1 | 187200im2 | \([0, 0, 0, -2029260, -1109107600]\) | \(38686490446661/141927552\) | \(3390347195449344000\) | \([2]\) | \(5505024\) | \(2.4161\) | |
187200.k2 | 187200im1 | \([0, 0, 0, -186060, 498800]\) | \(29819839301/17252352\) | \(412121976274944000\) | \([2]\) | \(2752512\) | \(2.0695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.k have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.k do not have complex multiplication.Modular form 187200.2.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.