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

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

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

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

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

Isogeny class 17424.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
17424.5-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 8\) , \( 4\bigr] \)
17424.5-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
17424.5-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -10 a + 88\) , \( 220 a + 92\bigr] \)
17424.5-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 10 a + 88\) , \( -220 a + 92\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph