Base field \(\Q(\sqrt{21}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).
Elliptic curves in class 153.1-b over \(\Q(\sqrt{21}) \)
Isogeny class 153.1-b contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
153.1-b1 | \( \bigl[1\) , \( a\) , \( a + 1\) , \( a - 2\) , \( -3\bigr] \) |
153.1-b2 | \( \bigl[1\) , \( a\) , \( a + 1\) , \( -14 a + 13\) , \( -24 a - 18\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)