Elliptic curve isogeny class 32448.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-32448.3-e
• Conductor: 32448.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 32448.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 32448.3-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
32448.3-e1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 120\) , \( -548 a + 256\bigr] \)
32448.3-e2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -115 a + 125\) , \( 107 a + 470\bigr] \)
32448.3-e3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -110 a + 235\) , \( 6369 a - 9303\bigr] \)
32448.3-e4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a + 10\) , \( -6 a + 12\bigr] \)
32448.3-e5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 30 a - 65\) , \( -115 a + 149\bigr] \)
32448.3-e6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 170 a - 365\) , \( 1465 a - 2271\bigr] \)
32448.3-e7	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 450 a - 965\) , \( -7471 a + 10697\bigr] \)
32448.3-e8	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2690 a - 5765\) , \( 102481 a - 152679\bigr] \)

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