Elliptic curve isogeny class 726.1-n over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-726.1-n
• Conductor: 726.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 726.1-n over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
726.1-n1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -11\) , \( 69\bigr] \)
726.1-n2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -1\) , \( -1\bigr] \)
726.1-n3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -21\) , \( 27\bigr] \)
726.1-n4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -351\) , \( 2337\bigr] \)

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