Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-2304.1-d
Conductor 2304.1
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 2304.1-d over \(\Q(\sqrt{5}) \)

Isogeny class 2304.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
2304.1-d1 \( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 2 \phi + 3\) , \( 13 \phi + 9\bigr] \)
2304.1-d2 \( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( -3 \phi - 17\) , \( -31 \phi + 14\bigr] \)
2304.1-d3 \( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( -3 \phi - 2\) , \( 2 \phi + 2\bigr] \)
2304.1-d4 \( \bigl[0\) , \( -\phi\) , \( 0\) , \( 3 \phi - 20\) , \( 31 \phi - 17\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph