Elliptic curve isogeny class 1296.3-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1296.3-b
• Conductor: 1296.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 1296.3-b over \(\Q(\sqrt{-2}) \)

Isogeny class 1296.3-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1296.3-b1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 36\) , \( 572\bigr] \)
1296.3-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \)
1296.3-b3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -9\) , \( -4\bigr] \)
1296.3-b4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -54\) , \( 176\bigr] \)
1296.3-b5	\( \bigl[a\) , \( -1\) , \( 0\) , \( 630 a + 756\) , \( -3276 a + 14324\bigr] \)
1296.3-b6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -630 a + 756\) , \( 3276 a + 14324\bigr] \)
1296.3-b7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -144\) , \( -598\bigr] \)
1296.3-b8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -864\) , \( 10220\bigr] \)

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