Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-27648.3-bp
Conductor 27648.3
Rank \( 0 \)

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 27648.3-bp over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.3-bp contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
27648.3-bp1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 31\) , \( 1737 a - 751\bigr] \)
27648.3-bp2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a + 1\) , \( -3 a - 1\bigr] \)
27648.3-bp3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a - 9\) , \( -23 a + 25\bigr] \)
27648.3-bp4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -98 a - 49\) , \( 457 a - 95\bigr] \)
27648.3-bp5 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1902 a - 1569\) , \( 45913 a - 623\bigr] \)
27648.3-bp6 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 782 a + 2911\) , \( 40761 a - 36463\bigr] \)
27648.3-bp7 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -258 a - 129\) , \( -1943 a + 1009\bigr] \)
27648.3-bp8 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 769\) , \( 29257 a - 10319\bigr] \)

Rank

Rank: \( 0 \)

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