Elliptic curve isogeny class 32400.3-g over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.3-g
• Conductor: 32400.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 32400.3-g over \(\Q(\sqrt{-2}) \)

Isogeny class 32400.3-g contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
32400.3-g1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -486\) , \( 13770\bigr] \)
32400.3-g2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 54\) , \( -486\bigr] \)
32400.3-g3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -16326\) , \( 117450\bigr] \)
32400.3-g4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2466\) , \( 41850\bigr] \)
32400.3-g5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -666\) , \( -5670\bigr] \)
32400.3-g6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -12006\) , \( 511434\bigr] \)
32400.3-g7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -10386\) , \( -402246\bigr] \)
32400.3-g8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -192006\) , \( 32479434\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph