Elliptic curve isogeny class 32448.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-32448.2-a
• Conductor: 32448.2
• Rank: \( 2 \)

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

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

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 32448.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 32448.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
32448.2-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 40 a + 112\) , \( 640 a - 596\bigr] \)
32448.2-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 12\) , \( -12\bigr] \)
32448.2-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 0\bigr] \)
32448.2-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -40 a + 152\) , \( -640 a + 44\bigr] \)