Elliptic curve isogeny class 12996.4-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-12996.4-c
• Conductor: 12996.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 12996.4-c over \(\Q(\sqrt{-2}) \)

Isogeny class 12996.4-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
12996.4-c1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 67 a + 518\) , \( 2964 a - 1443\bigr] \)
12996.4-c2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 254 a + 387\) , \( -1683 a + 4163\bigr] \)
12996.4-c3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -26 a + 46\) , \( 50 a + 137\bigr] \)
12996.4-c4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 42 a - 2\) , \( 96 a + 147\bigr] \)
12996.4-c5	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 19 a + 22\) , \( -52 a + 60\bigr] \)
12996.4-c6	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2 a + 33\) , \( 35 a - 55\bigr] \)
12996.4-c7	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 57 a - 112\) , \( 442 a - 45\bigr] \)
12996.4-c8	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -96 a - 3\) , \( -125 a + 515\bigr] \)

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