Elliptic curve isogeny class 4851.2-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-4851.2-a
• Conductor: 4851.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 4851.2-a over \(\Q(\sqrt{-11}) \)

Isogeny class 4851.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
4851.2-a1	\( \bigl[1\) , \( 1\) , \( 1\) , \( 31\) , \( -5578\bigr] \)
4851.2-a2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 126\) , \( 432\bigr] \)
4851.2-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -39\) , \( 36\bigr] \)
4851.2-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -284\) , \( -1924\bigr] \)
4851.2-a5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -34\) , \( 62\bigr] \)
4851.2-a6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -4519\) , \( -118810\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph