Elliptic curve isogeny class 36864.2-bd over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-36864.2-bd
• Conductor: 36864.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 36864.2-bd over \(\Q(\sqrt{-11}) \)

Isogeny class 36864.2-bd contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36864.2-bd1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -43 a - 82\) , \( 208 a + 215\bigr] \)
36864.2-bd2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a + 3\) , \( -3 a + 12\bigr] \)
36864.2-bd3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a - 2\) , \( 15\bigr] \)
36864.2-bd4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 37 a - 2\) , \( 64 a + 87\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph