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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 47190.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.y1 | 47190u4 | \([1, 0, 1, -19411549, 32915975816]\) | \(456612868287073618849/12544848030000\) | \(22223963520874830000\) | \([2]\) | \(2949120\) | \(2.8157\) | |
47190.y2 | 47190u3 | \([1, 0, 1, -5414269, -4384324408]\) | \(9908022260084596129/1047363281250000\) | \(1855467941894531250000\) | \([2]\) | \(2949120\) | \(2.8157\) | |
47190.y3 | 47190u2 | \([1, 0, 1, -1261549, 471035816]\) | \(125337052492018849/18404100000000\) | \(32603985800100000000\) | \([2, 2]\) | \(1474560\) | \(2.4691\) | |
47190.y4 | 47190u1 | \([1, 0, 1, 132371, 40035752]\) | \(144794100308831/474439680000\) | \(-840498833940480000\) | \([2]\) | \(737280\) | \(2.1225\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.y have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.y do not have complex multiplication.Modular form 47190.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.