Elliptic curve isogeny class 192.1-d over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-192.1-d
• Conductor: 192.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 20 & 4 & 10 & 2 & 20 & 4 \\ 5 & 1 & 4 & 20 & 2 & 10 & 4 & 20 \\ 20 & 4 & 1 & 20 & 2 & 10 & 4 & 5 \\ 4 & 20 & 20 & 1 & 10 & 2 & 5 & 4 \\ 10 & 2 & 2 & 10 & 1 & 5 & 2 & 10 \\ 2 & 10 & 10 & 2 & 5 & 1 & 10 & 2 \\ 20 & 4 & 4 & 5 & 2 & 10 & 1 & 20 \\ 4 & 20 & 5 & 4 & 10 & 2 & 20 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 192.1-d contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
192.1-d1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -160 a - 396\) , \( -1920 a - 4686\bigr] \)
192.1-d2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4\) , \( 8 a + 18\bigr] \)
192.1-d3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4 a - 13\) , \( -10 a - 26\bigr] \)
192.1-d4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -139 a - 470\) , \( -2021 a - 4290\bigr] \)
192.1-d5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 16\) , \( 20 a - 50\bigr] \)
192.1-d6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 648 a - 1616\) , \( -13940 a + 34110\bigr] \)
192.1-d7	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -29 a - 70\) , \( 107 a + 262\bigr] \)
192.1-d8	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -2614 a - 6413\) , \( -116564 a - 285510\bigr] \)