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

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

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

Curve label	Weierstrass Coefficients
3072.1-bq1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 528 a - 912\) , \( 8064 a - 13968\bigr] \)
3072.1-bq2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 32 a - 56\) , \( -142 a + 246\bigr] \)
3072.1-bq3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 118 a - 202\) , \( -744 a + 1288\bigr] \)
3072.1-bq4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -212 a + 368\) , \( -4380 a + 7588\bigr] \)

Rank

Rank: \( 1 \)

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