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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-17424.5-k
• 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-k over \(\Q(\sqrt{-2}) \)

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

Curve label	Weierstrass Coefficients
17424.5-k1	\( \bigl[a\) , \( 0\) , \( a\) , \( 175\) , \( 266\bigr] \)
17424.5-k2	\( \bigl[a\) , \( 0\) , \( a\) , \( -45\) , \( 46\bigr] \)
17424.5-k3	\( \bigl[a\) , \( 0\) , \( a\) , \( -25\) , \( -46\bigr] \)
17424.5-k4	\( \bigl[a\) , \( 0\) , \( a\) , \( -585\) , \( 5554\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph