Elliptic curve isogeny class 50700.2-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50700.2-f
• Conductor: 50700.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 50700.2-f over \(\Q(\sqrt{-3}) \)

Isogeny class 50700.2-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
50700.2-f1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -53378 a + 53377\) , \( -5124652\bigr] \)
50700.2-f2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 3997 a - 3998\) , \( 3998\bigr] \)
50700.2-f3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -16003 a + 16002\) , \( 27998\bigr] \)
50700.2-f4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -872578 a + 872577\) , \( -313799212\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph