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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.5-e
• 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-e over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
27225.5-e1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -55 a - 85\) , \( -2079 a - 637\bigr] \)
27225.5-e2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 110 a - 140\) , \( -605 a + 155\bigr] \)
27225.5-e3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -880 a + 3215\) , \( -29469 a - 29677\bigr] \)
27225.5-e4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1870 a - 2505\) , \( -65725 a - 23385\bigr] \)

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