Elliptic curve isogeny class 1800.1-g over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1800.1-g
• Conductor: 1800.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1800.1-g over \(\Q(\sqrt{3}) \)

Isogeny class 1800.1-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1800.1-g1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 33\) , \( -55 a + 95\bigr] \)
1800.1-g2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a - 18\) , \( -7 a + 28\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph