![Copy content]()
sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([1, 0, 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 \(i\), with minimal polynomial
\( x^{2} + 1 \); class number \(1\).
![Copy content]()
sage:E = EllipticCurve([K([0,1]),K([1,0]),K([1,0]),K([-453,-806]),K([-21,-11194])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 10530.4-a have
rank \( 0 \).
![Copy content]()
sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 3 & 6 & 2 & 9 & 18 \\
3 & 1 & 2 & 6 & 3 & 6 \\
6 & 2 & 1 & 3 & 6 & 3 \\
2 & 6 & 3 & 1 & 18 & 9 \\
9 & 3 & 6 & 18 & 1 & 2 \\
18 & 6 & 3 & 9 & 2 & 1
\end{array}\right)\)
![Copy content]()
sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 10530.4-a over \(\Q(\sqrt{-1}) \)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 10530.4-a contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 10530.4-a1
| \( \bigl[i\) , \( 1\) , \( 1\) , \( -806 i - 453\) , \( -11194 i - 21\bigr] \)
|
| 10530.4-a2
| \( \bigl[i\) , \( 1\) , \( 1\) , \( -86 i + 42\) , \( 11 i - 354\bigr] \)
|
| 10530.4-a3
| \( \bigl[1\) , \( -1\) , \( i\) , \( 4 i + 132\) , \( -947 i + 678\bigr] \)
|
| 10530.4-a4
| \( \bigl[1\) , \( -1\) , \( i\) , \( -86 i - 1173\) , \( 19834 i - 22731\bigr] \)
|
| 10530.4-a5
| \( \bigl[i\) , \( 1\) , \( 1\) , \( 4 i - 3\) , \( 2 i - 3\bigr] \)
|
| 10530.4-a6
| \( \bigl[1\) , \( -1\) , \( i\) , \( 49 i - 48\) , \( -218 i + 93\bigr] \)
|
