Elliptic curve isogeny class 4356.2-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-4356.2-b
• Conductor: 4356.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 4356.2-b over \(\Q(\sqrt{-11}) \)

Isogeny class 4356.2-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
4356.2-b1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -23 a + 44\) , \( -4 a - 179\bigr] \)
4356.2-b2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 23 a + 20\) , \( 27 a - 163\bigr] \)
4356.2-b3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 23 a - 90\) , \( 269 a - 669\bigr] \)
4356.2-b4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -23 a - 66\) , \( -246 a - 333\bigr] \)
4356.2-b5	\( \bigl[1\) , \( 1\) , \( 0\) , \( -35\) , \( -51\bigr] \)
4356.2-b6	\( \bigl[1\) , \( 1\) , \( 0\) , \( -475\) , \( -4187\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 18 & 2 & 3 & 6 \\ 9 & 1 & 2 & 18 & 3 & 6 \\ 18 & 2 & 1 & 9 & 6 & 3 \\ 2 & 18 & 9 & 1 & 6 & 3 \\ 3 & 3 & 6 & 6 & 1 & 2 \\ 6 & 6 & 3 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph