Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-16.2-a
Conductor 16.2
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 16.2-a over \(\Q(\sqrt{33}) \)

Isogeny class 16.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
16.2-a1 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 31 a + 72\) , \( 26 a + 60\bigr] \)
16.2-a2 \( \bigl[a\) , \( a - 1\) , \( a\) , \( a\) , \( 130 a - 436\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph