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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-726.1-f
• Conductor: 726.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
726.1-f1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -32 a - 115\) , \( -444 a - 17\bigr] \)
726.1-f2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2728 a - 3850\) , \( -87888 a + 149212\bigr] \)
726.1-f3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 38568 a - 70410\) , \( -5632848 a + 9738972\bigr] \)
726.1-f4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -312 a - 2235\) , \( -23220 a - 14265\bigr] \)

Rank

Rank: \( 0 \)

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