Elliptic curve isogeny class 50176.3-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50176.3-g
• Conductor: 50176.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 50176.3-g over \(\Q(\sqrt{-3}) \)

Isogeny class 50176.3-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
50176.3-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 8\) , \( 0\bigr] \)
50176.3-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -20 a + 32\) , \( 0\bigr] \)
50176.3-g3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 55 a - 88\) , \( -252 a + 266\bigr] \)
50176.3-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 55 a - 88\) , \( 252 a - 266\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph