Elliptic curve isogeny class 27225.4-f over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.4-f
• Conductor: 27225.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 27225.4-f over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.4-f contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
27225.4-f1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 166 a - 142\) , \( 1009 a + 71\bigr] \)
27225.4-f2	\( \bigl[1\) , \( a\) , \( 0\) , \( 171 a - 86\) , \( -750 a - 1149\bigr] \)
27225.4-f3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a - 32\) , \( -3 a + 104\bigr] \)
27225.4-f4	\( \bigl[1\) , \( a\) , \( 0\) , \( 226 a - 581\) , \( 2143 a - 7386\bigr] \)
27225.4-f5	\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a + 24\) , \( -57 a + 39\bigr] \)
27225.4-f6	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 276 a + 243\) , \( 3044 a - 7244\bigr] \)
27225.4-f7	\( \bigl[1\) , \( a\) , \( 0\) , \( 2756 a - 1351\) , \( -49535 a - 62584\bigr] \)
27225.4-f8	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 2696 a - 2287\) , \( 63522 a + 18254\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 2 & 10 & 10 & 2 & 10 & 2 \\ 5 & 1 & 10 & 2 & 2 & 10 & 2 & 10 \\ 2 & 10 & 1 & 20 & 5 & 4 & 20 & 4 \\ 10 & 2 & 20 & 1 & 4 & 20 & 4 & 5 \\ 10 & 2 & 5 & 4 & 1 & 20 & 4 & 20 \\ 2 & 10 & 4 & 20 & 20 & 1 & 5 & 4 \\ 10 & 2 & 20 & 4 & 4 & 5 & 1 & 20 \\ 2 & 10 & 4 & 5 & 20 & 4 & 20 & 1 \end{array}\right)\)

Isogeny graph