Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28.2-a
Conductor 28.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 28.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 28.2-a contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
28.2-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
28.2-a2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -10 a + 15\) , \( -5 a - 16\bigr] \)
28.2-a3 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 9 a + 6\) , \( 4 a - 20\bigr] \)
28.2-a4 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 1\) , \( -a + 1\bigr] \)
28.2-a5 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
28.2-a6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
28.2-a7 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
28.2-a8 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 30 a - 40\) , \( -30 a - 154\bigr] \)
28.2-a9 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -31 a - 9\) , \( 29 a - 183\bigr] \)
28.2-a10 \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
28.2-a11 \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
28.2-a12 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph