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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-q
• 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-q over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
3072.1-q1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a - 10\) , \( -11 a + 19\bigr] \)
3072.1-q2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -16 a - 28\) , \( 44 a + 76\bigr] \)
3072.1-q3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -116 a - 208\) , \( -796 a - 1388\bigr] \)
3072.1-q4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -236 a - 408\) , \( 2820 a + 4884\bigr] \)

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