Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-882.2-a
Conductor 882.2
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 882.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 882.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
882.2-a1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
882.2-a2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \)
882.2-a3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
882.2-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
882.2-a5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -595 a + 4306\) , \( 75404 a + 34009\bigr] \)
882.2-a6 \( \bigl[1\) , \( 1\) , \( 1\) , \( 595 a + 4306\) , \( -75404 a + 34009\bigr] \)
882.2-a7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
882.2-a8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 8 & 16 & 16 & 2 & 4 \\ 8 & 1 & 2 & 4 & 2 & 2 & 4 & 8 \\ 4 & 2 & 1 & 2 & 4 & 4 & 2 & 4 \\ 8 & 4 & 2 & 1 & 8 & 8 & 4 & 8 \\ 16 & 2 & 4 & 8 & 1 & 4 & 8 & 16 \\ 16 & 2 & 4 & 8 & 4 & 1 & 8 & 16 \\ 2 & 4 & 2 & 4 & 8 & 8 & 1 & 2 \\ 4 & 8 & 4 & 8 & 16 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph