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sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([221, 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 \(a\), with minimal polynomial
\( x^{2} + 221 \); class number \(16\).
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sage:E = EllipticCurve([K([0,1]),K([1,0]),K([0,1]),K([921,0]),K([-1915,0])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The rank \(r\) of the
elliptic curves in class 98.1-h satisfy
\(0 \le r \le 1\).
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sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 9 & 3 & 6 & 18 & 2 \\
9 & 1 & 3 & 6 & 2 & 18 \\
3 & 3 & 1 & 2 & 6 & 6 \\
6 & 6 & 2 & 1 & 3 & 3 \\
18 & 2 & 6 & 3 & 1 & 9 \\
2 & 18 & 6 & 3 & 9 & 1
\end{array}\right)\)
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sage:E.isogeny_class().graph().plot(edge_labels=True)
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sage:E.isogeny_class().curves
Isogeny class 98.1-h contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 98.1-h1
| \( \bigl[a\) , \( 1\) , \( a\) , \( 921\) , \( -1915\bigr] \)
|
| 98.1-h2
| \( \bigl[a\) , \( 1\) , \( a\) , \( 1091\) , \( -5849\bigr] \)
|
| 98.1-h3
| \( \bigl[a\) , \( 1\) , \( a\) , \( 1096\) , \( -5933\bigr] \)
|
| 98.1-h4
| \( \bigl[a\) , \( 1\) , \( a\) , \( 1056\) , \( -5149\bigr] \)
|
| 98.1-h5
| \( \bigl[a\) , \( 1\) , \( a\) , \( 1081\) , \( -5681\bigr] \)
|
| 98.1-h6
| \( \bigl[a\) , \( 1\) , \( a\) , \( -1639\) , \( 98437\bigr] \)
|
