Elliptic curve isogeny class 27225.5-n over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.5-n
• Conductor: 27225.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 27225.5-n over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.5-n contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27225.5-n1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -685 a + 479\) , \( 657 a + 5287\bigr] \)
27225.5-n2	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 2780 a - 1501\) , \( 3924 a + 49243\bigr] \)
27225.5-n3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -410 a + 149\) , \( 3286 a - 6065\bigr] \)
27225.5-n4	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -8550 a + 7739\) , \( -169106 a + 696439\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph