Elliptic curve isogeny class 17600.2-d over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-17600.2-d
• Conductor: 17600.2
• Rank: \( 0 \)

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

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

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

Elliptic curves in class 17600.2-d over \(\Q(\sqrt{-11}) \)

Isogeny class 17600.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
17600.2-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2627\) , \( 269646\bigr] \)
17600.2-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -7547\) , \( -12986\bigr] \)
17600.2-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -5047\) , \( 137514\bigr] \)
17600.2-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -5042\) , \( 137801\bigr] \)