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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.8-bh
• 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-bh over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
22500.8-bh1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 776 a - 6939\) , \( -38024 a + 219847\bigr] \)
22500.8-bh2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -724 a - 1939\) , \( -22024 a - 25153\bigr] \)
22500.8-bh3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 26 a + 61\) , \( -24 a + 347\bigr] \)
22500.8-bh4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 26 a - 439\) , \( -1024 a + 3347\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph