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sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([2, -1, 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
\( x^{2} - x + 2 \); class number \(1\).
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sage:E = EllipticCurve([K([1,1]),K([0,-1]),K([1,1]),K([-788,532]),K([5572,-7480])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 13552.12-a have
rank \( 1 \).
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sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 8 & 4 & 4 \\
8 & 1 & 4 & 4 & 8 & 2 \\
2 & 4 & 1 & 4 & 2 & 2 \\
8 & 4 & 4 & 1 & 8 & 2 \\
4 & 8 & 2 & 8 & 1 & 4 \\
4 & 2 & 2 & 2 & 4 & 1
\end{array}\right)\)
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sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 13552.12-a over \(\Q(\sqrt{-7}) \)
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sage:E.isogeny_class().curves
Isogeny class 13552.12-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 13552.12-a1
| \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 532 a - 788\) , \( -7480 a + 5572\bigr] \)
|
| 13552.12-a2
| \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -110 a + 60\) , \( 351 a - 572\bigr] \)
|
| 13552.12-a3
| \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 32 a - 48\) , \( -120 a + 100\bigr] \)
|
| 13552.12-a4
| \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -70 a - 54\) , \( 494 a - 238\bigr] \)
|
| 13552.12-a5
| \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -15 a + 18\) , \( -8 a - 74\bigr] \)
|
| 13552.12-a6
| \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 36\) , \( 72 a - 20\bigr] \)
|
