Elliptic curve isogeny class 27.2-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27.2-a
• Conductor: 27.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 27.2-a over \(\Q(\sqrt{-11}) \)

Isogeny class 27.2-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
27.2-a1	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -7 a + 15\) , \( -3 a - 13\bigr] \)
27.2-a2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4 a + 15\) , \( 8 a + 3\bigr] \)
27.2-a3	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a\) , \( -2 a + 2\bigr] \)
27.2-a4	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( a\) , \( -a + 3\bigr] \)
27.2-a5	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -19 a + 15\) , \( 50 a - 96\bigr] \)
27.2-a6	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 3 a + 30\) , \( 51 a - 94\bigr] \)
27.2-a7	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -69 a + 255\) , \( 642 a + 522\bigr] \)
27.2-a8	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -97 a + 240\) , \( -381 a - 1012\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 2 & 10 & 10 & 2 & 10 & 2 \\ 5 & 1 & 10 & 2 & 2 & 10 & 2 & 10 \\ 2 & 10 & 1 & 5 & 20 & 4 & 20 & 4 \\ 10 & 2 & 5 & 1 & 4 & 20 & 4 & 20 \\ 10 & 2 & 20 & 4 & 1 & 20 & 4 & 5 \\ 2 & 10 & 4 & 20 & 20 & 1 & 5 & 4 \\ 10 & 2 & 20 & 4 & 4 & 5 & 1 & 20 \\ 2 & 10 & 4 & 20 & 5 & 4 & 20 & 1 \end{array}\right)\)

Isogeny graph