![Copy content]()
sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([57, 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
\( x^{2} + 57 \); class number \(4\).
![Copy content]()
sage:E = EllipticCurve([K([0,1]),K([-1,0]),K([0,0]),K([-93,0]),K([1595,0])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 98.1-c have
rank \( 0 \).
![Copy content]()
sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 9 & 3 & 6 & 18 & 2 \\
9 & 1 & 3 & 6 & 2 & 18 \\
3 & 3 & 1 & 2 & 6 & 6 \\
6 & 6 & 2 & 1 & 3 & 3 \\
18 & 2 & 6 & 3 & 1 & 9 \\
2 & 18 & 6 & 3 & 9 & 1
\end{array}\right)\)
![Copy content]()
sage:E.isogeny_class().graph().plot(edge_labels=True)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 98.1-c contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 98.1-c1
| \( \bigl[a\) , \( -1\) , \( 0\) , \( -93\) , \( 1595\bigr] \)
|
| 98.1-c2
| \( \bigl[a\) , \( -1\) , \( 0\) , \( 77\) , \( -129\bigr] \)
|
| 98.1-c3
| \( \bigl[a\) , \( -1\) , \( 0\) , \( 82\) , \( -148\bigr] \)
|
| 98.1-c4
| \( \bigl[a\) , \( -1\) , \( 0\) , \( 42\) , \( 116\bigr] \)
|
| 98.1-c5
| \( \bigl[a\) , \( -1\) , \( 0\) , \( 67\) , \( -91\bigr] \)
|
| 98.1-c6
| \( \bigl[a\) , \( -1\) , \( 0\) , \( -2653\) , \( 68667\bigr] \)
|
