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

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

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

Curve label	Weierstrass Coefficients
27225.5-l1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 110 a + 426\) , \( 2332 a - 3467\bigr] \)
27225.5-l2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -110 a + 536\) , \( -2332 a - 1135\bigr] \)
27225.5-l3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 41\) , \( -79\bigr] \)
27225.5-l4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -13\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph