Elliptic curve isogeny class 75625.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-75625.1-a
• Conductor: 75625.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 75625.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 75625.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
75625.1-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 20 a - 21\) , \( 22\bigr] \)
75625.1-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -105 a + 104\) , \( 272\bigr] \)
75625.1-a3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -730 a + 729\) , \( -7228\bigr] \)
75625.1-a4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -1480 a + 1479\) , \( 22272\bigr] \)

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