Elliptic curve isogeny class 142884.1-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-142884.1-d
• Conductor: 142884.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 142884.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 142884.1-d contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
142884.1-d1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 1076 a - 2872\) , \( -29522 a + 55494\bigr] \)
142884.1-d2	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 41 a - 112\) , \( 273 a - 472\bigr] \)
142884.1-d3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 851 a - 2272\) , \( -42657 a + 79610\bigr] \)
142884.1-d4	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 8\) , \( -2 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph