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

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

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

Curve label	Weierstrass Coefficients
3072.1-j1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 40 a - 56\) , \( -40 a + 72\bigr] \)
3072.1-j2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a - 36\) , \( 72 a - 120\bigr] \)
3072.1-j3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 320 a - 576\) , \( 4296 a - 7464\bigr] \)
3072.1-j4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1\) , \( 4 a - 2\bigr] \)

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