Elliptic curve isogeny class 800.1-j over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-800.1-j
• Conductor: 800.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 800.1-j over \(\Q(\sqrt{6}) \)

Isogeny class 800.1-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
800.1-j1	\( \bigl[0\) , \( a\) , \( 0\) , \( -140 a - 341\) , \( 2257 a + 5528\bigr] \)
800.1-j2	\( \bigl[a\) , \( a\) , \( 0\) , \( -189 a - 464\) , \( 966 a + 2366\bigr] \)
800.1-j3	\( \bigl[0\) , \( a\) , \( 0\) , \( -31\) , \( 19 a\bigr] \)
800.1-j4	\( \bigl[a\) , \( a\) , \( a\) , \( 191 a - 467\) , \( 1156 a - 2832\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph