Properties

Base field \(\Q(\sqrt{65}) \)
Label 2.2.65.1-8.1-a
Conductor 8.1
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{65}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 16 \); class number \(2\).

Elliptic curves in class 8.1-a over \(\Q(\sqrt{65}) \)

Isogeny class 8.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
8.1-a1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
8.1-a2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 407 a - 1861\) , \( 10141 a - 45965\bigr] \)
8.1-a3 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 23 a - 109\bigr] \)
8.1-a4 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 116\) , \( 204 a - 940\bigr] \)

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