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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.1-e
• Conductor: 37632.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
37632.1-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 a - 60\) , \( 40 a + 200\bigr] \)
37632.1-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 57 a - 70\) , \( 205 a - 142\bigr] \)
37632.1-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 47 a - 125\) , \( -3161 a - 133\bigr] \)
37632.1-e4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 5\) , \( 4 a + 2\bigr] \)
37632.1-e5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13 a + 35\) , \( 51 a - 9\bigr] \)
37632.1-e6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -73 a + 195\) , \( -769 a - 109\bigr] \)
37632.1-e7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -193 a + 515\) , \( 3639 a + 27\bigr] \)
37632.1-e8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1153 a + 3075\) , \( -51817 a - 3925\bigr] \)

Rank

Rank: \( 0 \)

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