Elliptic curve isogeny class 4761.4-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-4761.4-b
• Conductor: 4761.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 4761.4-b over \(\Q(\sqrt{-11}) \)

Isogeny class 4761.4-b contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
4761.4-b1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -41 a - 76\) , \( 266 a + 167\bigr] \)
4761.4-b2	\( \bigl[1\) , \( 0\) , \( a\) , \( -52 a - 56\) , \( -296 a - 30\bigr] \)
4761.4-b3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4 a - 11\) , \( 20 a - 12\bigr] \)
4761.4-b4	\( \bigl[1\) , \( 0\) , \( a\) , \( -7 a + 9\) , \( -7 a - 24\bigr] \)
4761.4-b5	\( \bigl[1\) , \( 0\) , \( a\) , \( 13 a - 256\) , \( -640 a + 1883\bigr] \)
4761.4-b6	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -151 a + 59\) , \( -471 a + 1865\bigr] \)
4761.4-b7	\( \bigl[1\) , \( 0\) , \( a\) , \( -837 a - 896\) , \( -18268 a - 2067\bigr] \)
4761.4-b8	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -651 a - 1251\) , \( 15607 a + 11805\bigr] \)

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