Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-1452.1-j
Conductor 1452.1
Rank \( 1 \)

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 1452.1-j over \(\Q(\sqrt{21}) \)

Isogeny class 1452.1-j contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
1452.1-j1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \)
1452.1-j2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \)
1452.1-j3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \)
1452.1-j4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph