Elliptic curve isogeny class 241.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-241.1-a
• Conductor: 241.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 241.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 241.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
241.1-a1	\( \bigl[1\) , \( a\) , \( a\) , \( -80 a + 85\) , \( -33 a - 241\bigr] \)
241.1-a2	\( \bigl[1\) , \( a\) , \( a\) , \( -5 a + 5\) , \( -a - 2\bigr] \)
241.1-a3	\( \bigl[1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \)
241.1-a4	\( \bigl[1\) , \( a\) , \( a\) , \( -10 a + 5\) , \( -13 a + 9\bigr] \)

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