![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([1,1]),K([-1,0]),K([1,1]),K([405,-663]),K([-10065,4843])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 13552.10-c have
rank \( 0 \).
![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 13552.10-c over \(\Q(\sqrt{-7}) \)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 13552.10-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 13552.10-c1
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -663 a + 405\) , \( 4843 a - 10065\bigr] \)
|
| 13552.10-c2
| \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 96 a + 22\) , \( 35 a + 616\bigr] \)
|
| 13552.10-c3
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -43 a + 25\) , \( 83 a - 153\bigr] \)
|
| 13552.10-c4
| \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 22 a + 111\) , \( -273 a + 575\bigr] \)
|
| 13552.10-c5
| \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 16 a - 8\) , \( 48 a + 32\bigr] \)
|
| 13552.10-c6
| \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 12 a - 39\) , \( -81 a + 67\bigr] \)
|
