Elliptic curve isogeny class 144.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-144.1-b
• Conductor: 144.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 144.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[a\) , \( 0\) , \( a\) , \( 510 a - 817\) , \( -7986 a + 11650\bigr] \)
144.1-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 22\bigr] \)
144.1-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
144.1-b4	\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \)
144.1-b5	\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 4\bigr] \)
144.1-b6	\( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -28\bigr] \)
144.1-b7	\( \bigl[a\) , \( 0\) , \( a\) , \( -97\) , \( 346\bigr] \)
144.1-b8	\( \bigl[a\) , \( 0\) , \( a\) , \( -510 a - 817\) , \( 7986 a + 11650\bigr] \)

Rank

Rank: \( 0 \)

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