Elliptic curve isogeny class 600.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-600.1-a
• Conductor: 600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 600.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 600.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
600.1-a1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 6\) , \( 3 a + 6\bigr] \)
600.1-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -18 a - 29\) , \( 13 a + 23\bigr] \)
600.1-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -138 a - 239\) , \( -1187 a - 2059\bigr] \)
600.1-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -218 a - 379\) , \( 2213 a + 3833\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph