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

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

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

Curve label	Weierstrass Coefficients
726.1-b1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -170 a + 292\) , \( -4270 a + 7394\bigr] \)
726.1-b2	\( \bigl[1\) , \( a\) , \( 1\) , \( 3340899 a - 5786606\) , \( 4432110178 a - 7676640013\bigr] \)
726.1-b3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 276575 a - 479053\) , \( 104522175 a - 181037729\bigr] \)
726.1-b4	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -66 a - 147\) , \( 441 a + 826\bigr] \)

Rank

Rank: \( 0 \)

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