Elliptic curve isogeny class 891.3-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-891.3-b
• Conductor: 891.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 891.3-b over \(\Q(\sqrt{-11}) \)

Isogeny class 891.3-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
891.3-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 391\) , \( -1092\bigr] \)
891.3-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -104\) , \( -102\bigr] \)
891.3-b3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -59\) , \( 186\bigr] \)
891.3-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -450 a + 4576\) , \( -65628 a + 3012\bigr] \)
891.3-b5	\( \bigl[1\) , \( -1\) , \( 1\) , \( 450 a + 4126\) , \( 65628 a - 62616\bigr] \)
891.3-b6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1319\) , \( -18084\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 2 & 2 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 8 & 8 & 4 \\ 2 & 4 & 8 & 1 & 4 & 8 \\ 2 & 4 & 8 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph