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sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([1, 0, 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 \(i\), with minimal polynomial
\( x^{2} + 1 \); class number \(1\).
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sage:E = EllipticCurve([K([0,1]),K([0,-1]),K([1,0]),K([-6674,-134]),K([-212803,-2410])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 42250.6-f have
rank \( 0 \).
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sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 3 & 6 & 2 & 9 & 18 \\
3 & 1 & 2 & 6 & 3 & 6 \\
6 & 2 & 1 & 3 & 6 & 3 \\
2 & 6 & 3 & 1 & 18 & 9 \\
9 & 3 & 6 & 18 & 1 & 2 \\
18 & 6 & 3 & 9 & 2 & 1
\end{array}\right)\)
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sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 42250.6-f over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 42250.6-f contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 42250.6-f1
| \( \bigl[i\) , \( -i\) , \( 1\) , \( -134 i - 6674\) , \( -2410 i - 212803\bigr] \)
|
| 42250.6-f2
| \( \bigl[i\) , \( -i\) , \( 1\) , \( -574 i - 379\) , \( 7251 i + 374\bigr] \)
|
| 42250.6-f3
| \( \bigl[i\) , \( -i\) , \( 1\) , \( -804 i + 511\) , \( 13935 i + 17862\bigr] \)
|
| 42250.6-f4
| \( \bigl[i\) , \( -i\) , \( 1\) , \( 6986 i - 4834\) , \( -450954 i - 375811\bigr] \)
|
| 42250.6-f5
| \( \bigl[i\) , \( -i\) , \( 1\) , \( 36 i + 16\) , \( 30 i + 27\bigr] \)
|
| 42250.6-f6
| \( \bigl[i\) , \( -i\) , \( 1\) , \( 481 i + 131\) , \( 1536 i + 4119\bigr] \)
|
