Elliptic curve isogeny class 37632.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.3-e
• Conductor: 37632.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 37632.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.3-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
37632.3-e1	\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 70\) , \( -205 a + 63\bigr] \)
37632.3-e2	\( \bigl[0\) , \( a\) , \( 0\) , \( -68 a + 60\) , \( -40 a + 240\bigr] \)
37632.3-e3	\( \bigl[0\) , \( a\) , \( 0\) , \( -78 a + 125\) , \( 3161 a - 3294\bigr] \)
37632.3-e4	\( \bigl[0\) , \( a\) , \( 0\) , \( -3 a + 5\) , \( -4 a + 6\bigr] \)
37632.3-e5	\( \bigl[0\) , \( a\) , \( 0\) , \( 22 a - 35\) , \( -51 a + 42\bigr] \)
37632.3-e6	\( \bigl[0\) , \( a\) , \( 0\) , \( 122 a - 195\) , \( 769 a - 878\bigr] \)
37632.3-e7	\( \bigl[0\) , \( a\) , \( 0\) , \( 322 a - 515\) , \( -3639 a + 3666\bigr] \)
37632.3-e8	\( \bigl[0\) , \( a\) , \( 0\) , \( 1922 a - 3075\) , \( 51817 a - 55742\bigr] \)

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