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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-32448.2-d
• Conductor: 32448.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
32448.2-d1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -75 a + 110\) , \( 171 a + 266\bigr] \)
32448.2-d2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 5\) , \( 14\bigr] \)
32448.2-d3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -60\) , \( 144\bigr] \)
32448.2-d4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 75 a + 35\) , \( -171 a + 437\bigr] \)

Rank

Rank: \( 1 \)

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