Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-28.1-a
Conductor 28.1
Rank not recorded

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

Isogeny class 28.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
28.1-a1 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 852 a - 2388\) , \( -20118 a + 56153\bigr] \)
28.1-a2 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2 a - 8\) , \( 8 a - 25\bigr] \)
28.1-a3 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -23 a + 62\) , \( -161 a + 447\bigr] \)
28.1-a4 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 177 a - 498\) , \( -1497 a + 4175\bigr] \)
28.1-a5 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 52 a - 148\) , \( 346 a - 969\bigr] \)
28.1-a6 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 13652 a - 38228\) , \( -1309846 a + 3656537\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph