Elliptic curve isogeny class 1032.4-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1032.4-a
• Conductor: 1032.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 1032.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1032.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1032.4-a1	\( \bigl[a\) , \( a\) , \( 0\) , \( -a + 10\) , \( -6 a - 3\bigr] \)
1032.4-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( 9 a + 10\) , \( -10 a - 47\bigr] \)
1032.4-a3	\( \bigl[a\) , \( a\) , \( 0\) , \( -a\) , \( 1\bigr] \)
1032.4-a4	\( \bigl[a\) , \( a\) , \( 0\) , \( -11 a + 170\) , \( -546 a - 135\bigr] \)

Rank

Rank: \( 0 \)

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