Elliptic curve isogeny class 17424.5-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-17424.5-b
• Conductor: 17424.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 17424.5-b over \(\Q(\sqrt{-2}) \)

Isogeny class 17424.5-b contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
17424.5-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -40220\) , \( -3122472\bigr] \)
17424.5-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -2000 a + 5580\) , \( 102688 a + 124808\bigr] \)
17424.5-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( 2000 a + 5580\) , \( -102688 a + 124808\bigr] \)
17424.5-b4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -13900 a - 39900\) , \( 2250008 a - 3329992\bigr] \)
17424.5-b5	\( \bigl[a\) , \( 1\) , \( 0\) , \( 13900 a - 39900\) , \( -2250008 a - 3329992\bigr] \)
17424.5-b6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 460\) , \( 4488\bigr] \)
17424.5-b7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -180\) , \( 648\bigr] \)
17424.5-b8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -40260\) , \( -3115992\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 10 & 10 & 2 & 2 & 5 & 10 & 2 \\ 10 & 1 & 4 & 20 & 5 & 2 & 4 & 20 \\ 10 & 4 & 1 & 5 & 20 & 2 & 4 & 20 \\ 2 & 20 & 5 & 1 & 4 & 10 & 20 & 4 \\ 2 & 5 & 20 & 4 & 1 & 10 & 20 & 4 \\ 5 & 2 & 2 & 10 & 10 & 1 & 2 & 10 \\ 10 & 4 & 4 & 20 & 20 & 2 & 1 & 5 \\ 2 & 20 & 20 & 4 & 4 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph