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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([-1,0]),K([0,0]),K([806,1432]),K([25788,-258])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 16640.4-g 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 16640.4-g over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 16640.4-g contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 16640.4-g1
| \( \bigl[0\) , \( -1\) , \( 0\) , \( 1432 i + 806\) , \( -258 i + 25788\bigr] \)
|
| 16640.4-g2
| \( \bigl[0\) , \( -1\) , \( 0\) , \( 152 i - 74\) , \( -914 i - 52\bigr] \)
|
| 16640.4-g3
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -8 i - 234\) , \( -1682 i - 2164\bigr] \)
|
| 16640.4-g4
| \( \bigl[0\) , \( -1\) , \( 0\) , \( 152 i + 2086\) , \( 54526 i + 46268\bigr] \)
|
| 16640.4-g5
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -8 i + 6\) , \( -2 i - 4\bigr] \)
|
| 16640.4-g6
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -88 i + 86\) , \( -162 i - 516\bigr] \)
|
