Elliptic curve isogeny class 1089.1-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-1089.1-a
• Conductor: 1089.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 1089.1-a over \(\Q(\sqrt{-11}) \)

Isogeny class 1089.1-a contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
1089.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 328 a - 992\) , \( 5020 a - 10528\bigr] \)
1089.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a - 2\) , \( -2 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph