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

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-198.1-c
• Conductor: 198.1
• Rank: \( 1 \)

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

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

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

Isogeny class 198.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
198.1-c1	\( \bigl[a\) , \( 0\) , \( a\) , \( -10058\) , \( 380252\bigr] \)
198.1-c2	\( \bigl[a\) , \( 0\) , \( a\) , \( 112\) , \( -448\bigr] \)
198.1-c3	\( \bigl[a\) , \( 0\) , \( a\) , \( -48\) , \( -128\bigr] \)
198.1-c4	\( \bigl[a\) , \( 0\) , \( a\) , \( -10068\) , \( 379432\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph