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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([2864,-1612]),K([-52092,-51060])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 66560.4-p 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 66560.4-p over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 66560.4-p contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 66560.4-p1
| \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -1612 i + 2864\) , \( -51060 i - 52092\bigr] \)
|
| 66560.4-p2
| \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 148 i + 304\) , \( 1932 i - 1724\bigr] \)
|
| 66560.4-p3
| \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 468 i - 16\) , \( 7692 i + 964\bigr] \)
|
| 66560.4-p4
| \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -4172 i + 304\) , \( -201588 i + 16516\bigr] \)
|
| 66560.4-p5
| \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -12 i - 16\) , \( 12 i + 4\bigr] \)
|
| 66560.4-p6
| \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -172 i - 176\) , \( 1356 i + 708\bigr] \)
|
