Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-1089.1-f
Conductor 1089.1
Rank \( 2 \)

Related objects

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

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

Elliptic curves in class 1089.1-f over \(\Q(\sqrt{21}) \)

Isogeny class 1089.1-f contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1089.1-f1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -2\) , \( 0\bigr] \)
1089.1-f2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -17\) , \( 30\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph