Elliptic curve isogeny class 27225.3-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.3-b
• Conductor: 27225.3
• Rank bounds: 0...1

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

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

Elliptic curves in class 27225.3-b over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.3-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
27225.3-b1	\( \bigl[a\) , \( 0\) , \( a\) , \( 2311 a + 1983\) , \( -19721 a + 138914\bigr] \)
27225.3-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( a + 3\) , \( a - 10\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph