Elliptic curve isogeny class 108.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-108.2-a
• Conductor: 108.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 108.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 108.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
108.2-a1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -59 a + 4\) , \( 122 a - 261\bigr] \)
108.2-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -48 a + 49\) , \( 7 a + 265\bigr] \)
108.2-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 7\) , \( 11 a + 4\bigr] \)
108.2-a4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9\) , \( 5 a - 2\bigr] \)
108.2-a5	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
108.2-a6	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -4 a - 1\) , \( a - 7\bigr] \)
108.2-a7	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 11 a + 14\) , \( 16 a - 19\bigr] \)
108.2-a8	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 13 a + 37\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\ 12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\ 4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\ 12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\ 6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\ 2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\ 4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\ 3 & 4 & 12 & 4 & 2 & 6 & 12 & 1 \end{array}\right)\)

Isogeny graph