Elliptic curve isogeny class 20736.3-h over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-20736.3-h
• Conductor: 20736.3
• Rank: \( 1 \)

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

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

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

Elliptic curves in class 20736.3-h over \(\Q(\sqrt{-11}) \)

Isogeny class 20736.3-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
20736.3-h1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 720 a - 1911\) , \( -16748 a + 27022\bigr] \)
20736.3-h2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -720 a - 1191\) , \( -16748 a - 10274\bigr] \)
20736.3-h3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( -620 a + 310\bigr] \)
20736.3-h4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 69\) , \( -116 a + 58\bigr] \)