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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-600.1-c
• Conductor: 600.1
• Rank: \( 0 \)

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

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

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

Isogeny class 600.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
600.1-c1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 80 a - 140\) , \( 4500 a - 7800\bigr] \)
600.1-c2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -80 a + 140\) , \( -150 a + 260\bigr] \)
600.1-c3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a - 35\) , \( 0\bigr] \)
600.1-c4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 200 a - 350\) , \( 2160 a - 3744\bigr] \)
600.1-c5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
600.1-c6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 3200 a - 5600\) , \( 132660 a - 229944\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph