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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-600.1-d
• 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-d over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
600.1-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 4 a + 7\) , \( 0\bigr] \)
600.1-d2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -16 a - 28\) , \( -30 a - 52\bigr] \)
600.1-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -136 a - 238\) , \( 1050 a + 1820\bigr] \)
600.1-d4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -216 a - 378\) , \( -2430 a - 4212\bigr] \)

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