Elliptic curve isogeny class 1568.2-i over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1568.2-i
• Conductor: 1568.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1568.2-i over \(\Q(\sqrt{2}) \)

Isogeny class 1568.2-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1568.2-i1	\( \bigl[a\) , \( 1\) , \( a\) , \( -55 a - 97\) , \( 1397 a + 1934\bigr] \)
1568.2-i2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -55 a - 96\) , \( -1452 a - 2031\bigr] \)
1568.2-i3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 9\) , \( 0\bigr] \)
1568.2-i4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 9\) , \( 0\bigr] \)
1568.2-i5	\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 24\) , \( 44 a - 56\bigr] \)
1568.2-i6	\( \bigl[a\) , \( 1\) , \( a\) , \( 11 a - 25\) , \( -33 a + 31\bigr] \)
1568.2-i7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -44 a - 84\) , \( 286 a + 208\bigr] \)
1568.2-i8	\( \bigl[a\) , \( 1\) , \( a\) , \( -44 a - 85\) , \( -330 a - 293\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph