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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([1,-1]),K([1,1]),K([39,1744]),K([21608,20027])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 37570.10-c have
rank \( 1 \).
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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 37570.10-c over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 37570.10-c contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 37570.10-c1
| \( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 1744 i + 39\) , \( 20027 i + 21608\bigr] \)
|
| 37570.10-c2
| \( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 104 i - 146\) , \( -666 i + 546\bigr] \)
|
| 37570.10-c3
| \( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -126 i - 216\) , \( -2996 i - 716\bigr] \)
|
| 37570.10-c4
| \( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 1184 i + 1879\) , \( 78699 i - 744\bigr] \)
|
| 37570.10-c5
| \( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -6 i + 9\) , \( -11 i + 4\bigr] \)
|
| 37570.10-c6
| \( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -41 i + 124\) , \( -572 i - 217\bigr] \)
|
