Elliptic curve isogeny class 756.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-756.1-a
• Conductor: 756.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 9 & 3 & 9 \\ 9 & 1 & 9 & 3 & 9 \\ 9 & 9 & 1 & 3 & 9 \\ 3 & 3 & 3 & 1 & 3 \\ 9 & 9 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 756.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 756.1-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
756.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 699 a - 305\) , \( -4326 a - 2344\bigr] \)
756.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 249 a - 260\) , \( 1740 a - 922\bigr] \)
756.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -a\) , \( 0\bigr] \)
756.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 5\) , \( -6 a - 4\bigr] \)
756.1-a5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -111 a + 145\) , \( -186 a - 472\bigr] \)