Elliptic curve isogeny class 45625.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-45625.1-a
• Conductor: 45625.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 45625.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 45625.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
45625.1-a1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 245 a - 366\) , \( -2388 a + 2264\bigr] \)
45625.1-a2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 134\) , \( -638 a + 264\bigr] \)
45625.1-a3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 9\) , \( -13 a + 14\bigr] \)
45625.1-a4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 120 a - 366\) , \( -3763 a + 1639\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph