Elliptic curve isogeny class 1536.1-g over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1536.1-g
• Conductor: 1536.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1536.1-g over \(\Q(\sqrt{3}) \)

Isogeny class 1536.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1536.1-g1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a - 24\) , \( -108 a - 180\bigr] \)
1536.1-g2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4240 a - 7344\) , \( -196380 a + 340140\bigr] \)
1536.1-g3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 265 a - 459\) , \( -3000 a + 5196\bigr] \)
1536.1-g4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 340 a - 594\) , \( -1050 a + 1812\bigr] \)

Rank

Rank: \( 0 \)

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