Elliptic curve isogeny class 3072.1-bi over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-bi
• Conductor: 3072.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3072.1-bi over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-bi contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3072.1-bi1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 7\) , \( -9 a + 17\bigr] \)
3072.1-bi2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 22 a - 38\) , \( 0\bigr] \)
3072.1-bi3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -88 a + 152\) , \( -240 a + 416\bigr] \)
3072.1-bi4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 212 a - 368\) , \( 2404 a - 4164\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph