Elliptic curve isogeny class 30276.2-e over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-30276.2-e
• Conductor: 30276.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 30276.2-e over \(\Q(\sqrt{-11}) \)

Isogeny class 30276.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30276.2-e1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( -2\bigr] \)
30276.2-e2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -50\) , \( 86\bigr] \)
30276.2-e3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -20\) , \( -34\bigr] \)
30276.2-e4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -310\) , \( -2122\bigr] \)

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