Elliptic curve isogeny class 22500.8-bi over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.8-bi
• Conductor: 22500.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 22500.8-bi over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.8-bi contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
22500.8-bi1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -777 a - 6162\) , \( 38024 a + 181823\bigr] \)
22500.8-bi2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -27 a - 412\) , \( 1024 a + 2323\bigr] \)
22500.8-bi3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -27 a + 88\) , \( 24 a + 323\bigr] \)
22500.8-bi4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 723 a - 2662\) , \( 22024 a - 47177\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph