Elliptic curve isogeny class 27648.3-bh over number field \(\Q(\sqrt{-2}) \)

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

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 5 & 10 & 10 & 10 & 2 \\ 2 & 1 & 4 & 10 & 20 & 20 & 5 & 4 \\ 2 & 4 & 1 & 10 & 20 & 5 & 20 & 4 \\ 5 & 10 & 10 & 1 & 2 & 2 & 2 & 10 \\ 10 & 20 & 20 & 2 & 1 & 4 & 4 & 5 \\ 10 & 20 & 5 & 2 & 4 & 1 & 4 & 20 \\ 10 & 5 & 20 & 2 & 4 & 4 & 1 & 20 \\ 2 & 4 & 4 & 10 & 5 & 20 & 20 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 27648.3-bh over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.3-bh contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
27648.3-bh1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 318 a + 159\) , \( 765 a + 3825\bigr] \)
27648.3-bh2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 58 a + 1019\) , \( 13113 a + 3357\bigr] \)
27648.3-bh3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 498 a - 741\) , \( -9927 a + 12573\bigr] \)
27648.3-bh4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 1\) , \( -3 a - 15\bigr] \)
27648.3-bh5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 14 a + 7\) , \( 5 a + 25\bigr] \)
27648.3-bh6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -62 a + 59\) , \( 9 a - 387\bigr] \)
27648.3-bh7	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -22 a - 101\) , \( -151 a - 323\bigr] \)
27648.3-bh8	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1294 a + 647\) , \( -6555 a - 32775\bigr] \)