Elliptic curve isogeny class 28900.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-28900.1-b
• Conductor: 28900.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 28900.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 28900.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
28900.1-b1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 2473 a\) , \( 52716\bigr] \)
28900.1-b2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -16312 a\) , \( -159988\bigr] \)
28900.1-b3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 4168 a\) , \( -20724\bigr] \)
28900.1-b4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 2553 a\) , \( 49452\bigr] \)

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