Elliptic curve isogeny class 16335.3-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-16335.3-b
• Conductor: 16335.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 16335.3-b over \(\Q(\sqrt{-11}) \)

Isogeny class 16335.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
16335.3-b1	\( \bigl[a\) , \( a\) , \( 0\) , \( -26 a\) , \( -43 a + 130\bigr] \)
16335.3-b2	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 109 a - 51\) , \( 30 a + 630\bigr] \)
16335.3-b3	\( \bigl[a\) , \( a\) , \( 0\) , \( -136 a - 165\) , \( 1134 a + 559\bigr] \)
16335.3-b4	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 54 a - 51\) , \( -201 a + 36\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph