Elliptic curve isogeny class 27.3-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27.3-a
• Conductor: 27.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 27.3-a over \(\Q(\sqrt{-11}) \)

Isogeny class 27.3-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
27.3-a1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 5 a + 11\) , \( -4 a + 22\bigr] \)
27.3-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 6 a + 7\) , \( 16 a - 34\bigr] \)
27.3-a3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1\) , \( 3\bigr] \)
27.3-a4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( a - 3\) , \( -3\bigr] \)
27.3-a5	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -4 a + 32\) , \( -23 a - 31\bigr] \)
27.3-a6	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 20 a - 4\) , \( -31 a - 50\bigr] \)
27.3-a7	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 96 a + 142\) , \( 619 a - 1681\bigr] \)
27.3-a8	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 70 a + 186\) , \( -573 a + 1350\bigr] \)

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