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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.8-a
• Conductor: 27225.8
• Rank: \( 1 \)

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

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

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

Isogeny class 27225.8-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27225.8-a1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 119 a - 96\) , \( -562 a - 402\bigr] \)
27225.8-a2	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 4 a - 11\) , \( -13 a - 33\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph