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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([0,0]),K([-1259,-2238]),K([1489,-50752])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 16250.6-l 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 16250.6-l over \(\Q(\sqrt{-1}) \)
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sage:E.isogeny_class().curves
Isogeny class 16250.6-l contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 16250.6-l1
| \( \bigl[1\) , \( i - 1\) , \( 0\) , \( -2238 i - 1259\) , \( -50752 i + 1489\bigr] \)
|
| 16250.6-l2
| \( \bigl[1\) , \( i - 1\) , \( 0\) , \( -238 i + 116\) , \( 248 i - 1636\bigr] \)
|
| 16250.6-l3
| \( \bigl[1\) , \( i - 1\) , \( 0\) , \( 12 i + 366\) , \( 4498 i - 3386\bigr] \)
|
| 16250.6-l4
| \( \bigl[1\) , \( i - 1\) , \( 0\) , \( -238 i - 3259\) , \( -92752 i + 107489\bigr] \)
|
| 16250.6-l5
| \( \bigl[1\) , \( i - 1\) , \( 0\) , \( 12 i - 9\) , \( -2 i - 11\bigr] \)
|
| 16250.6-l6
| \( \bigl[1\) , \( i - 1\) , \( 0\) , \( 137 i - 134\) , \( 873 i - 386\bigr] \)
|
