Elliptic curve isogeny class 27225.7-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.7-a
• Conductor: 27225.7
• Rank: \( 2 \)

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

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

Elliptic curves in class 27225.7-a over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.7-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27225.7-a1	\( \bigl[1\) , \( -a\) , \( a\) , \( -114 a - 416\) , \( -1269 a - 3143\bigr] \)
27225.7-a2	\( \bigl[1\) , \( -a\) , \( a\) , \( -4 a - 31\) , \( -26 a - 30\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph