Elliptic curve isogeny class 1296.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1296.1-b
• Conductor: 1296.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1296.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 1296.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1296.1-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4590 a - 7344\) , \( 220212 a - 321908\bigr] \)
1296.1-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( -572\bigr] \)
1296.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \)
1296.1-b4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -9\) , \( 4\bigr] \)
1296.1-b5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -54\) , \( -176\bigr] \)
1296.1-b6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -144\) , \( 598\bigr] \)
1296.1-b7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -864\) , \( -10220\bigr] \)
1296.1-b8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -4590 a - 7344\) , \( -220212 a - 321908\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph