Elliptic curve isogeny class 147.1-g over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-147.1-g
• Conductor: 147.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 147.1-g over \(\Q(\sqrt{6}) \)

Isogeny class 147.1-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
147.1-g1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \)
147.1-g2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
147.1-g3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)
147.1-g4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \)
147.1-g5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \)
147.1-g6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph