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

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

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

Curve label	Weierstrass Coefficients
726.1-j1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 13 a - 22\) , \( 43 a - 76\bigr] \)
726.1-j2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3638 a - 6317\) , \( 156916 a - 271777\bigr] \)
726.1-j3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 223 a - 402\) , \( 2427 a - 4194\bigr] \)
726.1-j4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 168 a - 567\) , \( 2394 a - 2643\bigr] \)

Rank

Rank: \( 0 \)

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