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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([1,0]),K([0,-1]),K([0,1]),K([1471,939]),K([-20896,18545])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 37570.12-b 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 37570.12-b over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 37570.12-b contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 37570.12-b1
| \( \bigl[1\) , \( -i\) , \( i\) , \( 939 i + 1471\) , \( 18545 i - 20896\bigr] \)
|
| 37570.12-b2
| \( \bigl[1\) , \( -i\) , \( i\) , \( 179 i + 6\) , \( 658 i + 757\bigr] \)
|
| 37570.12-b3
| \( \bigl[1\) , \( -i\) , \( i\) , \( 109 i - 224\) , \( -194 i + 3077\bigr] \)
|
| 37570.12-b4
| \( \bigl[1\) , \( -i\) , \( i\) , \( -901 i + 2031\) , \( -10607 i - 78368\bigr] \)
|
| 37570.12-b5
| \( \bigl[1\) , \( -i\) , \( i\) , \( -11 i + 1\) , \( i + 2\bigr] \)
|
| 37570.12-b6
| \( \bigl[1\) , \( -i\) , \( i\) , \( -126 i + 36\) , \( -225 i + 498\bigr] \)
|
