Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-288.2-a
Conductor 288.2
Rank \( 1 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 288.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 288.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
288.2-a1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -5 a + 22\) , \( 26 a + 23\bigr] \)
288.2-a2 \( \bigl[a\) , \( 1\) , \( 0\) , \( 5 a + 22\) , \( -26 a + 23\bigr] \)
288.2-a3 \( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( 1\bigr] \)
288.2-a4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
288.2-a5 \( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \)
288.2-a6 \( \bigl[a\) , \( 1\) , \( a\) , \( -7\) , \( 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph