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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-bd
• Conductor: 3072.1
• Rank: \( 1 \)

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

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

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

Isogeny class 3072.1-bd contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3072.1-bd1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a + 15\) , \( -3158 a - 5469\bigr] \)
3072.1-bd2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -230 a + 399\) , \( 1578 a - 2733\bigr] \)
3072.1-bd3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 70 a - 121\) , \( 250 a - 433\bigr] \)
3072.1-bd4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 16\) , \( -12 a + 20\bigr] \)
3072.1-bd5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 970 a - 1681\) , \( 21970 a - 38053\bigr] \)
3072.1-bd6	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -12 a - 16\) , \( -84 a + 68\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph