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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.5-j
• Conductor: 27225.5
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
27225.5-j1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -169 a + 700\) , \( -2956 a - 2214\bigr] \)
27225.5-j2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 161 a + 260\) , \( 1378 a - 3886\bigr] \)
27225.5-j3	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -4 a + 40\) , \( -19 a - 102\bigr] \)
27225.5-j4	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -4 a - 15\) , \( -19 a - 3\bigr] \)

Rank

Rank: \( 1 \)

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