Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-2268.1-e
Conductor 2268.1
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 2268.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 2268.1-e contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
2268.1-e1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -141\) , \( 681\bigr] \)
2268.1-e2 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 52 a - 147\) , \( -882 a + 2462\bigr] \)
2268.1-e3 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 472 a + 850\) , \( -22302 a - 39958\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph