Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-17.2-a
Conductor 17.2
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 17.2-a over \(\Q(\sqrt{21}) \)

Isogeny class 17.2-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
17.2-a1 \( \bigl[a\) , \( 0\) , \( a\) , \( -2 a - 5\) , \( a + 1\bigr] \)
17.2-a2 \( \bigl[a\) , \( 0\) , \( a\) , \( 13 a + 20\) , \( -11 a - 22\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph