Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-324.1-b
Conductor 324.1
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 324.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 324.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
324.1-b1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
324.1-b2 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 67 a - 189\) , \( 702 a - 1960\bigr] \)
324.1-b3 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -8 a + 21\) , \( -18 a + 50\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph