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

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

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

Curve label	Weierstrass Coefficients
27225.5-m1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -2782 a + 1280\) , \( -3925 a + 53168\bigr] \)
27225.5-m2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 683 a - 205\) , \( -658 a + 5945\bigr] \)
27225.5-m3	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 408 a - 260\) , \( -3287 a - 2778\bigr] \)
27225.5-m4	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 8548 a - 810\) , \( 169105 a + 527334\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph