Elliptic curve isogeny class 34560.3-k over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-34560.3-k
• Conductor: 34560.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 34560.3-k over \(\Q(\sqrt{-11}) \)

Isogeny class 34560.3-k contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
34560.3-k1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 38 a - 3\) , \( 71 a + 110\bigr] \)
34560.3-k2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -157 a + 72\) , \( 607 a - 669\bigr] \)
34560.3-k3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 198 a + 237\) , \( 871 a - 3874\bigr] \)
34560.3-k4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -77 a + 72\) , \( -129 a + 531\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph