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

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

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

Curve label	Weierstrass Coefficients
726.1-k1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 563082 a - 975336\) , \( -303877939 a + 526332123\bigr] \)
726.1-k2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 115\) , \( -561\bigr] \)
726.1-k3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -45\) , \( -81\bigr] \)
726.1-k4	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 563642 a - 976306\) , \( -303245579 a + 525236843\bigr] \)

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