Elliptic curve isogeny class 71424.2-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-71424.2-f
• Conductor: 71424.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 71424.2-f over \(\Q(\sqrt{-3}) \)

Isogeny class 71424.2-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
71424.2-f1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -66 a + 387\) , \( -3009 a + 681\bigr] \)
71424.2-f2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a + 27\) , \( -45 a + 9\bigr] \)
71424.2-f3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 54 a - 93\) , \( -297 a + 153\bigr] \)
71424.2-f4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a + 12\) , \( 9 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph