Elliptic curve isogeny class 142884.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-142884.3-e
• Conductor: 142884.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 142884.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 142884.3-e contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
142884.3-e1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1796 a + 2873\) , \( 29521 a + 25973\bigr] \)
142884.3-e2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -71 a + 113\) , \( -274 a - 198\bigr] \)
142884.3-e3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1421 a + 2273\) , \( 42656 a + 36954\bigr] \)
142884.3-e4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4 a - 7\) , \( a - 1\bigr] \)

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