Elliptic curve isogeny class 27225.2-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.2-a
• Conductor: 27225.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 27225.2-a over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27225.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -120 a + 21\) , \( 584 a - 628\bigr] \)
27225.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -5 a - 9\) , \( 5 a - 25\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph