Elliptic curve isogeny class 108.1-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-108.1-b
• Conductor: 108.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 108.1-b over \(\Q(\sqrt{-11}) \)

Isogeny class 108.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
108.1-b1	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -21 a + 30\) , \( 6 a - 81\bigr] \)
108.1-b2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
108.1-b3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -a\) , \( 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph