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sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([-1, -1, 1]))
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pari:K = nfinit(Polrev(%s));
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magma:R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R!%s);
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oscar:Qx, x = polynomial_ring(QQ); K, a = number_field(Qx(%s))
Generator \(\phi\), with minimal polynomial
\( x^{2} - x - 1 \); class number \(1\).
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sage:E = EllipticCurve([K([1,0]),K([-1,0]),K([1,0]),K([-143,-657]),K([-308982,204734])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 3564.2-b have
rank \( 0 \).
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sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 8 & 2 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
8 & 4 & 2 & 1 & 4 & 8 \\
2 & 4 & 2 & 4 & 1 & 2 \\
4 & 8 & 4 & 8 & 2 & 1
\end{array}\right)\)
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sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 3564.2-b over \(\Q(\sqrt{5}) \)
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sage:E.isogeny_class().curves
Isogeny class 3564.2-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 3564.2-b1
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -657 \phi - 143\) , \( 204734 \phi - 308982\bigr] \)
|
| 3564.2-b2
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 67 \phi - 6\) , \( 220 \phi + 11\bigr] \)
|
| 3564.2-b3
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 67 \phi - 726\) , \( 5692 \phi - 4597\bigr] \)
|
| 3564.2-b4
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 3847 \phi - 9906\) , \( 197932 \phi - 400525\bigr] \)
|
| 3564.2-b5
| \( \bigl[1\) , \( -1\) , \( 1\) , \( 1773 \phi - 4193\) , \( 72866 \phi - 99030\bigr] \)
|
| 3564.2-b6
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -4437 \phi - 14003\) , \( 422966 \phi + 507498\bigr] \)
|
