Elliptic curve isogeny class 147.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-147.1-b
• Conductor: 147.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 147.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 147.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
147.1-b1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 3395 a - 6664\) , \( -153951 a + 275173\bigr] \)
147.1-b2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -34\) , \( 217\bigr] \)
147.1-b3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -54 a + 96\) , \( -55 a + 96\bigr] \)
147.1-b4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( 1\bigr] \)
147.1-b5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -39\) , \( -90\bigr] \)
147.1-b6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -49\) , \( 136\bigr] \)
147.1-b7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -784\) , \( 8515\bigr] \)
147.1-b8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -3395 a - 6664\) , \( 153951 a + 275173\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 16 & 4 & 2 & 4 \\ 8 & 1 & 8 & 4 & 8 & 2 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 16 & 8 & 4 & 2 & 1 & 4 & 8 & 16 \\ 4 & 2 & 4 & 2 & 4 & 1 & 2 & 4 \\ 2 & 4 & 8 & 4 & 8 & 2 & 1 & 2 \\ 4 & 8 & 16 & 8 & 16 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph