Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-180.1-a
Conductor 180.1
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{5}) \)

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

Elliptic curves in class 180.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 180.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
180.1-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \)
180.1-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
180.1-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \)
180.1-a4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
180.1-a5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
180.1-a6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
180.1-a7 \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \)
180.1-a8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph