Elliptic curve isogeny class 20736.3-bn over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-20736.3-bn
• Conductor: 20736.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 20736.3-bn over \(\Q(\sqrt{-11}) \)

Isogeny class 20736.3-bn contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
20736.3-bn1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 141\) , \( -4718\bigr] \)
20736.3-bn2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \)
20736.3-bn3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( 70\bigr] \)
20736.3-bn4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -219\) , \( -1190\bigr] \)
20736.3-bn5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -579\) , \( 5362\bigr] \)
20736.3-bn6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3459\) , \( -78302\bigr] \)

Rank

Rank: \( 1 \)

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