Elliptic curve isogeny class 722.1-g over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-722.1-g
• Conductor: 722.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 722.1-g over \(\Q(\sqrt{6}) \)

Isogeny class 722.1-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
722.1-g1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -311 a - 759\) , \( -4716 a - 11551\bigr] \)
722.1-g2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1711 a - 4189\) , \( 484528 a + 1186849\bigr] \)
722.1-g3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -189 a + 466\) , \( 17680 a - 43306\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph