Elliptic curve isogeny class 1568.3-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1568.3-b
• Conductor: 1568.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1568.3-b over \(\Q(\sqrt{2}) \)

Isogeny class 1568.3-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1568.3-b1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -a + 6\) , \( -1518 a - 2139\bigr] \)
1568.3-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( 44 a + 45\) , \( 110 a + 127\bigr] \)
1568.3-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -44 a - 66\) , \( 88 a + 120\bigr] \)
1568.3-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 26 a - 44\) , \( -40 a + 49\bigr] \)
1568.3-b5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a - 1\) , \( 99 a - 116\bigr] \)
1568.3-b6	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 381 a - 654\) , \( -5384 a + 7135\bigr] \)