Elliptic curve isogeny class 2304.2-d over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-2304.2-d
• Conductor: 2304.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 2304.2-d over \(\Q(\sqrt{-11}) \)

Isogeny class 2304.2-d contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
2304.2-d1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 85\) , \( 55 a - 275\bigr] \)
2304.2-d2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 80\) , \( 60 a + 300\bigr] \)
2304.2-d3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 5\) , \( -9 a - 3\bigr] \)
2304.2-d4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( -4 a + 12\bigr] \)
2304.2-d5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 76 a - 160\) , \( 668 a - 116\bigr] \)
2304.2-d6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -74 a - 85\) , \( 743 a - 467\bigr] \)
2304.2-d7	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -84 a - 1280\) , \( 2268 a + 17868\bigr] \)
2304.2-d8	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 86 a - 1365\) , \( 2183 a - 18771\bigr] \)

Rank

Rank: \( 1 \)

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