Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-768.1-q
Conductor 768.1
Rank \( 1 \)

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 768.1-q over \(\Q(\sqrt{21}) \)

Isogeny class 768.1-q contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
768.1-q1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 16\) , \( 180\bigr] \)
768.1-q2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
768.1-q3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( -4\bigr] \)
768.1-q4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -24\) , \( 36\bigr] \)
768.1-q5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \)
768.1-q6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph