Elliptic curve isogeny class 165.3-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-165.3-a
• Conductor: 165.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 165.3-a over \(\Q(\sqrt{-11}) \)

Isogeny class 165.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
165.3-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a - 4\) , \( -3\bigr] \)
165.3-a2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 6 a + 1\) , \( 5 a - 33\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph