Elliptic curve isogeny class 27648.2-bh over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.2-bh
• Conductor: 27648.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 27648.2-bh over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.2-bh contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
27648.2-bh1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 470 a - 37\) , \( -3705 a - 3939\bigr] \)
27648.2-bh2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 382 a - 389\) , \( 4615 a - 611\bigr] \)
27648.2-bh3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a + 13\) , \( -17 a + 31\bigr] \)
27648.2-bh4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 19\) , \( 3 a + 39\bigr] \)
27648.2-bh5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 22 a - 29\) , \( 79 a + 37\bigr] \)
27648.2-bh6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a + 3\) , \( -81 a - 27\bigr] \)
27648.2-bh7	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -90 a - 117\) , \( -393 a - 627\bigr] \)
27648.2-bh8	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -18 a + 171\) , \( 567 a - 243\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph