Elliptic curve isogeny class 50176.2-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50176.2-f
• Conductor: 50176.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 50176.2-f over \(\Q(\sqrt{-3}) \)

Isogeny class 50176.2-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
50176.2-f1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -79 a + 45\) , \( -145 a + 260\bigr] \)
50176.2-f2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 81 a - 35\) , \( -225 a - 80\bigr] \)
50176.2-f3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 15\) , \( -39 a + 12\bigr] \)
50176.2-f4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 260\) , \( -1950 a + 845\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph