Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-16.1-a
Conductor 16.1
Rank \( 0 \)

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 16.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 16.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -2\bigr] \)
16.1-a2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \)
16.1-a3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 13\) , \( 11 a - 31\bigr] \)
16.1-a4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( -16 a - 28\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph