![Copy content]()
sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([2, -1, 1]))
![Copy content]()
pari:K = nfinit(Polrev(%s));
![Copy content]()
magma:R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R!%s);
![Copy content]()
oscar:Qx, x = polynomial_ring(QQ); K, a = number_field(Qx(%s))
Generator \(a\), with minimal polynomial
\( x^{2} - x + 2 \); class number \(1\).
![Copy content]()
sage:E = EllipticCurve([K([0,0]),K([-1,0]),K([0,0]),K([593,-3283]),K([87207,-77889])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 25088.4-e have
rank \( 1 \).
![Copy content]()
sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 8 & 4 & 4 \\
8 & 1 & 4 & 4 & 8 & 2 \\
2 & 4 & 1 & 4 & 2 & 2 \\
8 & 4 & 4 & 1 & 8 & 2 \\
4 & 8 & 2 & 8 & 1 & 4 \\
4 & 2 & 2 & 2 & 4 & 1
\end{array}\right)\)
![Copy content]()
sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 25088.4-e over \(\Q(\sqrt{-7}) \)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 25088.4-e contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 25088.4-e1
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -3283 a + 593\) , \( -77889 a + 87207\bigr] \)
|
| 25088.4-e2
| \( \bigl[0\) , \( 1\) , \( 0\) , \( 378 a + 355\) , \( 2695 a - 8107\bigr] \)
|
| 25088.4-e3
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -203 a + 33\) , \( -1169 a + 1415\bigr] \)
|
| 25088.4-e4
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -34 a + 667\) , \( 5199 a - 5411\bigr] \)
|
| 25088.4-e5
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 78 a - 5\) , \( -243 a - 805\bigr] \)
|
| 25088.4-e6
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 106 a - 173\) , \( 747 a - 203\bigr] \)
|
