Elliptic curve isogeny class 4356.6-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-4356.6-a
• Conductor: 4356.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 4356.6-a over \(\Q(\sqrt{-2}) \)

Isogeny class 4356.6-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
4356.6-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 198 a - 120\) , \( 1458 a + 342\bigr] \)
4356.6-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( 121 a - 251\) , \( -1109 a + 1240\bigr] \)
4356.6-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 22 a + 15\) , \( -2 a + 74\bigr] \)
4356.6-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -6 a - 33\) , \( 24 a + 84\bigr] \)
4356.6-a5	\( \bigl[a\) , \( 1\) , \( a\) , \( 6 a - 16\) , \( -21 a + 11\bigr] \)
4356.6-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 13 a - 5\) , \( 26 a - 4\bigr] \)
4356.6-a7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -52 a - 30\) , \( 182 a + 56\bigr] \)
4356.6-a8	\( \bigl[a\) , \( 1\) , \( a\) , \( 11 a + 79\) , \( -145 a + 196\bigr] \)

Rank

Rank: \( 1 \)

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