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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-726.1-a
• 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-a over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
726.1-a1	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 239 a - 589\) , \( -14693 a + 35989\bigr] \)
726.1-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 39 a - 99\) , \( 57 a - 141\bigr] \)
726.1-a3	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -440 a - 1079\) , \( 7267 a + 17799\bigr] \)
726.1-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 7039 a - 17249\) , \( -494017 a + 1210089\bigr] \)

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