Elliptic curve isogeny class 27225.6-d over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.6-d
• Conductor: 27225.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 27225.6-d over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.6-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27225.6-d1	\( \bigl[0\) , \( a + 1\) , \( a\) , \( -21 a + 25\) , \( 11 a + 108\bigr] \)
27225.6-d2	\( \bigl[0\) , \( a + 1\) , \( a\) , \( 34 a - 85\) , \( -165 a + 185\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph