Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-27648.2-v
Conductor 27648.2
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 27648.2-v over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.2-v contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
27648.2-v1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -62 a + 31\) , \( 1737 a + 751\bigr] \)
27648.2-v2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 1\) , \( -3 a + 1\bigr] \)
27648.2-v3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 18 a - 9\) , \( -23 a - 25\bigr] \)
27648.2-v4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 98 a - 49\) , \( 457 a + 95\bigr] \)
27648.2-v5 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -782 a + 2911\) , \( 40761 a + 36463\bigr] \)
27648.2-v6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1902 a - 1569\) , \( 45913 a + 623\bigr] \)
27648.2-v7 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 258 a - 129\) , \( -1943 a - 1009\bigr] \)
27648.2-v8 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1538 a - 769\) , \( 29257 a + 10319\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph