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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-147.1-h
• 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-h over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
147.1-h1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 680 a - 1669\) , \( -42286 a + 103577\bigr] \)
147.1-h2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -20 a + 46\) , \( -20 a + 47\bigr] \)
147.1-h3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -82 a - 199\) , \( 117 a + 287\bigr] \)
147.1-h4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 780 a - 1914\) , \( 18600 a - 45563\bigr] \)
147.1-h5	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 980 a - 2404\) , \( -25948 a + 63557\bigr] \)
147.1-h6	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 15680 a - 38419\) , \( -1670290 a + 4091357\bigr] \)

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