Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-578.1-d
Conductor 578.1
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 578.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 578.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
578.1-d1 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 60 a - 150\) , \( 258 a - 634\bigr] \)
578.1-d2 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2262 a - 5540\) , \( 62881 a + 154026\bigr] \)
578.1-d3 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 860 a - 2110\) , \( 21650 a - 53034\bigr] \)
578.1-d4 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2062 a - 5050\) , \( 79317 a + 194286\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph