Elliptic curve isogeny class 45625.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-45625.2-a
• Conductor: 45625.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 45625.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 45625.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
45625.2-a1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -121 a + 366\) , \( 2388 a - 124\bigr] \)
45625.2-a2	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 129 a - 134\) , \( 638 a - 374\bigr] \)
45625.2-a3	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -246 a + 366\) , \( 3763 a - 2124\bigr] \)
45625.2-a4	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4 a - 9\) , \( 13 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph