Base field \(\Q(\sqrt{3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 746.1-c over \(\Q(\sqrt{3}) \)
Isogeny class 746.1-c contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 746.1-c1 | \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2\) , \( a + 1\bigr] \) |
| 746.1-c2 | \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3\) , \( -31 a - 41\bigr] \) |