Elliptic curve isogeny class 726.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-726.1-b
• Conductor: 726.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 726.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 726.1-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
726.1-b1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \)
726.1-b2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
726.1-b3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
726.1-b4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph