Elliptic curve isogeny class 150.1-e over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-150.1-e
• Conductor: 150.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 150.1-e over \(\Q(\sqrt{6}) \)

Isogeny class 150.1-e contains 12 curves linked by isogenies of degrees dividing 24.

Curve label	Weierstrass Coefficients
150.1-e1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 885 a - 2449\) , \( -24162 a + 61154\bigr] \)
150.1-e2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \)
150.1-e3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
150.1-e4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 1310 a - 1414\) , \( -25288 a + 58064\bigr] \)
150.1-e5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \)
150.1-e6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
150.1-e7	\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
150.1-e8	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1310 a - 1414\) , \( 25288 a + 58064\bigr] \)
150.1-e9	\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
150.1-e10	\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \)
150.1-e11	\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \)
150.1-e12	\( \bigl[1\) , \( 0\) , \( 1\) , \( -885 a - 2449\) , \( 24162 a + 61154\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\ 24 & 1 & 3 & 8 & 4 & 12 & 6 & 8 & 2 & 12 & 4 & 24 \\ 8 & 3 & 1 & 24 & 12 & 4 & 2 & 24 & 6 & 4 & 12 & 8 \\ 3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\ 6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\ 8 & 12 & 4 & 24 & 12 & 1 & 2 & 24 & 6 & 4 & 3 & 8 \\ 4 & 6 & 2 & 12 & 6 & 2 & 1 & 12 & 3 & 2 & 6 & 4 \\ 12 & 8 & 24 & 4 & 2 & 24 & 12 & 1 & 4 & 6 & 8 & 3 \\ 12 & 2 & 6 & 4 & 2 & 6 & 3 & 4 & 1 & 6 & 2 & 12 \\ 2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\ 24 & 4 & 12 & 8 & 4 & 3 & 6 & 8 & 2 & 12 & 1 & 24 \\ 4 & 24 & 8 & 12 & 6 & 8 & 4 & 3 & 12 & 2 & 24 & 1 \end{array}\right)\)

Isogeny graph