Elliptic curve isogeny class 37632.2-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.2-g
• Conductor: 37632.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 37632.2-g over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.2-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
37632.2-g1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 48\) , \( -48\bigr] \)
37632.2-g2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12\) , \( 0\bigr] \)
37632.2-g3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 80 a + 488\) , \( 5312 a - 3760\bigr] \)
37632.2-g4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 10\bigr] \)
37632.2-g5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -80 a + 568\) , \( -5312 a + 1552\bigr] \)
37632.2-g6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -152\) , \( -672\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph