Elliptic curve isogeny class 225.5-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-225.5-b
• Conductor: 225.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.5-b over \(\Q(\sqrt{-11}) \)

Isogeny class 225.5-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
225.5-b1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -385 a - 144\) , \( -4471 a + 3234\bigr] \)
225.5-b2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -980 a + 901\) , \( 6920 a - 26670\bigr] \)
225.5-b3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a - 9\) , \( -70 a + 75\bigr] \)
225.5-b4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4\) , \( -5 a + 7\bigr] \)
225.5-b5	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 210 a + 71\) , \( 826 a - 3542\bigr] \)
225.5-b6	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -65 a + 46\) , \( 71 a - 372\bigr] \)
225.5-b7	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
225.5-b8	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 25 a - 79\) , \( -160 a + 247\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 2 & 4 & 8 & 4 & 8 & 8 \\ 8 & 1 & 4 & 8 & 4 & 2 & 16 & 16 \\ 2 & 4 & 1 & 2 & 4 & 2 & 4 & 4 \\ 4 & 8 & 2 & 1 & 8 & 4 & 2 & 2 \\ 8 & 4 & 4 & 8 & 1 & 2 & 16 & 16 \\ 4 & 2 & 2 & 4 & 2 & 1 & 8 & 8 \\ 8 & 16 & 4 & 2 & 16 & 8 & 1 & 4 \\ 8 & 16 & 4 & 2 & 16 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph