Elliptic curve isogeny class 1200.1-j over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1200.1-j
• Conductor: 1200.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1200.1-j over \(\Q(\sqrt{3}) \)

Isogeny class 1200.1-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1200.1-j1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -3 a + 11\) , \( -1254 a + 2173\bigr] \)
1200.1-j2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 18 a - 36\) , \( -84 a + 141\bigr] \)
1200.1-j3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 72 a - 119\) , \( -429 a + 744\bigr] \)
1200.1-j4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 147 a - 269\) , \( 666 a - 1221\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph