Elliptic curve isogeny class 2156.1-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-2156.1-b
• Conductor: 2156.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2156.1-b over \(\Q(\sqrt{-11}) \)

Isogeny class 2156.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2156.1-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -89\bigr] \)
2156.1-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -604\) , \( 2343\bigr] \)
2156.1-b3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -324\) , \( -2137\bigr] \)
2156.1-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5164\) , \( -141529\bigr] \)

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