Elliptic curve isogeny class 37632.1-k over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.1-k
• Conductor: 37632.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 37632.1-k over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.1-k contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
37632.1-k1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 68 a - 8\) , \( -40 a - 200\bigr] \)
37632.1-k2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 13 a + 57\) , \( -205 a + 142\bigr] \)
37632.1-k3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 78 a + 47\) , \( 3161 a + 133\bigr] \)
37632.1-k4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 3 a + 2\) , \( -4 a - 2\bigr] \)
37632.1-k5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -22 a - 13\) , \( -51 a + 9\bigr] \)
37632.1-k6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -122 a - 73\) , \( 769 a + 109\bigr] \)
37632.1-k7	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -322 a - 193\) , \( -3639 a - 27\bigr] \)
37632.1-k8	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1922 a - 1153\) , \( 51817 a + 3925\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\ 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph