Elliptic curve isogeny class 500.2-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-500.2-b
• Conductor: 500.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 500.2-b over \(\Q(\sqrt{6}) \)

Isogeny class 500.2-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
500.2-b1	\( \bigl[a\) , \( -a\) , \( a\) , \( 625 a - 1535\) , \( -9420 a + 23077\bigr] \)
500.2-b2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 80 a - 62\) , \( -1030 a - 1224\bigr] \)
500.2-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -14 a - 74\) , \( 36 a - 49\bigr] \)
500.2-b4	\( \bigl[a\) , \( -a\) , \( 0\) , \( -110 a - 272\) , \( 786 a + 1970\bigr] \)
500.2-b5	\( \bigl[a\) , \( -a\) , \( 0\) , \( -35 a - 97\) , \( -174 a - 420\bigr] \)
500.2-b6	\( \bigl[a\) , \( -a\) , \( a\) , \( 210 a - 520\) , \( 2766 a - 6774\bigr] \)
500.2-b7	\( \bigl[0\) , \( -a\) , \( 0\) , \( 126 a - 314\) , \( 242 a - 595\bigr] \)
500.2-b8	\( \bigl[a\) , \( -a\) , \( a\) , \( -165 a + 355\) , \( 10016 a - 24399\bigr] \)

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