Elliptic curve isogeny class 4356.4-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-4356.4-a
• Conductor: 4356.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 4356.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 4356.4-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
4356.4-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( -121 a - 251\) , \( 1109 a + 1240\bigr] \)
4356.4-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -198 a - 120\) , \( -1458 a + 342\bigr] \)
4356.4-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a - 33\) , \( -24 a + 84\bigr] \)
4356.4-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -22 a + 15\) , \( 2 a + 74\bigr] \)
4356.4-a5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -13 a - 5\) , \( -26 a - 4\bigr] \)
4356.4-a6	\( \bigl[a\) , \( 1\) , \( a\) , \( -6 a - 16\) , \( 21 a + 11\bigr] \)
4356.4-a7	\( \bigl[a\) , \( 1\) , \( a\) , \( -11 a + 79\) , \( 145 a + 196\bigr] \)
4356.4-a8	\( \bigl[a\) , \( 1\) , \( 0\) , \( 52 a - 30\) , \( -182 a + 56\bigr] \)

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