Elliptic curve isogeny class 135.6-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-135.6-a
• Conductor: 135.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 135.6-a over \(\Q(\sqrt{-11}) \)

Isogeny class 135.6-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
135.6-a1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6 a - 5\) , \( -6 a - 9\bigr] \)
135.6-a2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \)
135.6-a3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -24 a + 40\) , \( -25 a - 15\bigr] \)
135.6-a4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -14 a + 15\) , \( -10 a + 69\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph