Elliptic curve isogeny class 578.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-578.1-a
• Conductor: 578.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 578.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 578.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
578.1-a1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( 1\bigr] \)
578.1-a2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -113\) , \( -329\bigr] \)
578.1-a3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \)
578.1-a4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -103\) , \( -411\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph