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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-726.1-m
• 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-m over \(\Q(\sqrt{3}) \)

Isogeny class 726.1-m contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
726.1-m1	\( \bigl[a\) , \( -1\) , \( a\) , \( -42\) , \( 555\bigr] \)
726.1-m2	\( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( -21\bigr] \)
726.1-m3	\( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -5\bigr] \)
726.1-m4	\( \bigl[a\) , \( -1\) , \( a\) , \( -82\) , \( 283\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph