Elliptic curve isogeny class 17424.4-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-17424.4-e
• Conductor: 17424.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 17424.4-e over \(\Q(\sqrt{-2}) \)

Isogeny class 17424.4-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
17424.4-e1	\( \bigl[a\) , \( 0\) , \( a\) , \( -121 a - 251\) , \( -1109 a - 1239\bigr] \)
17424.4-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -198 a - 120\) , \( 1458 a - 342\bigr] \)
17424.4-e3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 6 a - 33\) , \( 24 a - 84\bigr] \)
17424.4-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -22 a + 15\) , \( -2 a - 74\bigr] \)
17424.4-e5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -13 a - 5\) , \( 26 a + 4\bigr] \)
17424.4-e6	\( \bigl[a\) , \( 0\) , \( a\) , \( -6 a - 16\) , \( -21 a - 10\bigr] \)
17424.4-e7	\( \bigl[a\) , \( 0\) , \( a\) , \( -11 a + 79\) , \( -145 a - 195\bigr] \)
17424.4-e8	\( \bigl[a\) , \( 0\) , \( 0\) , \( 52 a - 30\) , \( 182 a - 56\bigr] \)

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