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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.7-b
• Conductor: 27225.7
• 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 27225.7-b over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.7-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
27225.7-b1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2313 a + 4294\) , \( 19720 a + 119193\bigr] \)
27225.7-b2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a + 4\) , \( -2 a - 9\bigr] \)

Rank

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

Isogeny matrix

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

Isogeny graph