Base field \(\Q(\sqrt{3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).
Elliptic curves in class 1458.1-g over \(\Q(\sqrt{3}) \)
Isogeny class 1458.1-g contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 1458.1-g1 | \( \bigl[a\) , \( 0\) , \( 1\) , \( -2 a - 3\) , \( -2 a - 4\bigr] \) |
| 1458.1-g2 | \( \bigl[1\) , \( -1\) , \( a + 1\) , \( a + 1\) , \( -a - 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
