Elliptic curve isogeny class 127449.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-127449.3-b
• Conductor: 127449.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 127449.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 127449.3-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
127449.3-b1	\( \bigl[1\) , \( -1\) , \( a\) , \( 16 a - 6\) , \( 830 a + 711\bigr] \)
127449.3-b2	\( \bigl[1\) , \( -1\) , \( a\) , \( 16 a - 6\) , \( -10 a - 3\bigr] \)
127449.3-b3	\( \bigl[1\) , \( -1\) , \( a\) , \( 136 a - 51\) , \( 275 a + 276\bigr] \)
127449.3-b4	\( \bigl[1\) , \( -1\) , \( a\) , \( 2176 a - 816\) , \( 19400 a + 17157\bigr] \)

Rank

Rank: \( 0 \)

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