Elliptic curve isogeny class 27225.8-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.8-b
• Conductor: 27225.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 27225.8-b over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.8-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27225.8-b1	\( \bigl[a\) , \( -a\) , \( a\) , \( 9 a + 19\) , \( 10 a + 20\bigr] \)
27225.8-b2	\( \bigl[a\) , \( -a\) , \( a\) , \( -46 a - 91\) , \( 219 a + 141\bigr] \)
27225.8-b3	\( \bigl[a\) , \( -a\) , \( a\) , \( -321 a - 641\) , \( -4896 a - 4644\bigr] \)
27225.8-b4	\( \bigl[a\) , \( -a\) , \( a\) , \( -651 a - 1301\) , \( 16070 a + 13330\bigr] \)

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