![Copy content]()
sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([-3, 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 \(a\), with minimal polynomial
\( x^{2} - 3 \); class number \(1\).
![Copy content]()
sage:E = EllipticCurve([K([1,0]),K([1,0]),K([0,0]),K([-1226,645]),K([21843,-12039])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 363.1-a have
rank \( 0 \).
![Copy content]()
sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 8 & 2 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
8 & 4 & 2 & 1 & 4 & 8 \\
2 & 4 & 2 & 4 & 1 & 2 \\
4 & 8 & 4 & 8 & 2 & 1
\end{array}\right)\)
![Copy content]()
sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 363.1-a over \(\Q(\sqrt{3}) \)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 363.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 363.1-a1
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 645 a - 1226\) , \( -12039 a + 21843\bigr] \)
|
| 363.1-a2
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
|
| 363.1-a3
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
|
| 363.1-a4
| \( \bigl[a\) , \( a - 1\) , \( a\) , \( 365 a - 633\) , \( 4716 a - 8169\bigr] \)
|
| 363.1-a5
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)
|
| 363.1-a6
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -645 a - 1226\) , \( 12039 a + 21843\bigr] \)
|
