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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1200.1-g
• Conductor: 1200.1
• Rank: \( 0 \)

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

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

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

Isogeny class 1200.1-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1200.1-g1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -17 a + 29\) , \( -48 a + 83\bigr] \)
1200.1-g2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 83 a - 151\) , \( -288 a + 491\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph