Elliptic curve isogeny class 784.1-k over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-784.1-k
• Conductor: 784.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 784.1-k over \(\Q(\sqrt{6}) \)

Isogeny class 784.1-k contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
784.1-k1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13642 a - 33423\) , \( 1370379 a + 3356729\bigr] \)
784.1-k2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -42 a - 103\) , \( -437 a - 1071\bigr] \)
784.1-k3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -358 a + 877\) , \( -9467 a + 23189\bigr] \)
784.1-k4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 2842 a - 6963\) , \( -107643 a + 263669\bigr] \)
784.1-k5	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 842 a - 2063\) , \( 20245 a - 49591\bigr] \)
784.1-k6	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 218442 a - 535183\) , \( -87132427 a + 213430329\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph