Elliptic curve isogeny class 198.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-198.1-a
• Conductor: 198.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 198.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 198.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
198.1-a1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -11\) , \( 69\bigr] \)
198.1-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1\) , \( -1\bigr] \)
198.1-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -21\) , \( 27\bigr] \)
198.1-a4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -351\) , \( 2337\bigr] \)

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