Elliptic curve isogeny class 1089.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1089.3-a
• Conductor: 1089.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1089.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1089.3-a contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
1089.3-a1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -a - 4\) , \( a - 5\bigr] \)
1089.3-a2	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -141 a - 24\) , \( -767 a + 1837\bigr] \)