Properties

Base field \(\Q(\sqrt{-23}) \)
Label 2.0.23.1-6.4-a
Conductor 6.4
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 6 \); class number \(3\).

Elliptic curves in class 6.4-a over \(\Q(\sqrt{-23}) \)

Isogeny class 6.4-a contains 8 curves linked by isogenies of degrees dividing 28.

Curve label Weierstrass Coefficients
6.4-a1 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 206 a + 403\) , \( -1402 a + 7012\bigr] \)
6.4-a2 \( \bigl[a\) , \( a\) , \( a\) , \( 8 a - 178\) , \( -154 a + 999\bigr] \)
6.4-a3 \( \bigl[a\) , \( a\) , \( a\) , \( 88 a - 98\) , \( 582 a + 1991\bigr] \)
6.4-a4 \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -4 a - 17\) , \( -9 a\bigr] \)
6.4-a5 \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( 1\bigr] \)
6.4-a6 \( \bigl[a\) , \( a\) , \( a\) , \( -2 a + 2\) , \( 3\bigr] \)
6.4-a7 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( -a + 5\bigr] \)
6.4-a8 \( \bigl[a\) , \( a\) , \( a\) , \( -12 a + 22\) , \( 8 a - 45\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 28 & 14 & 7 & 28 \\ 2 & 1 & 2 & 2 & 14 & 7 & 14 & 14 \\ 4 & 2 & 1 & 4 & 28 & 14 & 28 & 7 \\ 4 & 2 & 4 & 1 & 7 & 14 & 28 & 28 \\ 28 & 14 & 28 & 7 & 1 & 2 & 4 & 4 \\ 14 & 7 & 14 & 14 & 2 & 1 & 2 & 2 \\ 7 & 14 & 28 & 28 & 4 & 2 & 1 & 4 \\ 28 & 14 & 7 & 28 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph