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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([-1,0]),K([0,1]),K([-453,805]),K([21,-11194])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 10530.1-a 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 10530.1-a over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 10530.1-a contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 10530.1-a1
| \( \bigl[1\) , \( -1\) , \( i\) , \( 805 i - 453\) , \( -11194 i + 21\bigr] \)
|
| 10530.1-a2
| \( \bigl[1\) , \( -1\) , \( i\) , \( 85 i + 42\) , \( 11 i + 354\bigr] \)
|
| 10530.1-a3
| \( \bigl[i\) , \( 1\) , \( 1\) , \( -5 i + 132\) , \( -947 i - 678\bigr] \)
|
| 10530.1-a4
| \( \bigl[i\) , \( 1\) , \( 1\) , \( 85 i - 1173\) , \( 19834 i + 22731\bigr] \)
|
| 10530.1-a5
| \( \bigl[1\) , \( -1\) , \( i\) , \( -5 i - 3\) , \( 2 i + 3\bigr] \)
|
| 10530.1-a6
| \( \bigl[i\) , \( 1\) , \( 1\) , \( -50 i - 48\) , \( -218 i - 93\bigr] \)
|
