Elliptic curve isogeny class 450.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-450.1-a
• Conductor: 450.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 450.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 450.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
450.1-a1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -11\) , \( 51\bigr] \)
450.1-a2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \)
450.1-a3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -451\) , \( 91\bigr] \)
450.1-a4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -66\) , \( 126\bigr] \)
450.1-a5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -16\) , \( -44\bigr] \)
450.1-a6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -331\) , \( 2035\bigr] \)
450.1-a7	\( \bigl[a\) , \( 0\) , \( 0\) , \( -286\) , \( -2150\bigr] \)
450.1-a8	\( \bigl[a\) , \( 0\) , \( 0\) , \( -5331\) , \( 145035\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph