Elliptic curve isogeny class 3025.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-3025.1-a
• Conductor: 3025.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3025.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 3025.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3025.1-a1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \)
3025.1-a2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -4 a + 4\) , \( 3\bigr] \)
3025.1-a3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -29 a + 29\) , \( -52\bigr] \)
3025.1-a4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -59 a + 59\) , \( 190\bigr] \)

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