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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([0,0]),K([1,-1]),K([0,0]),K([-961,9264]),K([-201179,-276097])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 26000.6-e have
rank \( 0 \).
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sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 6 & 18 & 2 & 9 & 3 \\
6 & 1 & 3 & 3 & 6 & 2 \\
18 & 3 & 1 & 9 & 2 & 6 \\
2 & 3 & 9 & 1 & 18 & 6 \\
9 & 6 & 2 & 18 & 1 & 3 \\
3 & 2 & 6 & 6 & 3 & 1
\end{array}\right)\)
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sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 26000.6-e over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 26000.6-e contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 26000.6-e1
| \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 9264 i - 961\) , \( -276097 i - 201179\bigr] \)
|
| 26000.6-e2
| \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -248 i - 201\) , \( -2001 i - 549\bigr] \)
|
| 26000.6-e3
| \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 12 i - 21\) , \( -29 i + 47\bigr] \)
|
| 26000.6-e4
| \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -2308 i + 219\) , \( 25771 i - 36553\bigr] \)
|
| 26000.6-e5
| \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -16 i - 1\) , \( 23 i - 19\bigr] \)
|
| 26000.6-e6
| \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 124 i + 19\) , \( -469 i + 25\bigr] \)
|
