Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-450.1-d
Conductor 450.1
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 450.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 450.1-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
450.1-d1 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 154 a - 375\) , \( 1701 a - 4165\bigr] \)
450.1-d2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 6\) , \( 0\bigr] \)
450.1-d3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -24\) , \( 18\bigr] \)
450.1-d4 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2643 a - 6492\) , \( -105330 a - 258022\bigr] \)
450.1-d5 \( \bigl[1\) , \( -1\) , \( 0\) , \( 15 a - 264\) , \( -681 a + 414\bigr] \)
450.1-d6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -15 a - 264\) , \( 681 a + 414\bigr] \)
450.1-d7 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2553 a - 6252\) , \( -113724 a - 278566\bigr] \)
450.1-d8 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 2644 a - 6495\) , \( 98835 a - 242161\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 12 & 3 & 2 & 4 \\ 12 & 4 & 2 & 12 & 1 & 4 & 6 & 3 \\ 12 & 4 & 2 & 3 & 4 & 1 & 6 & 12 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 3 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph