Elliptic curve isogeny class 116964.3-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-116964.3-d
• Conductor: 116964.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 116964.3-d over \(\Q(\sqrt{-3}) \)

Isogeny class 116964.3-d contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
116964.3-d1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -538 a + 58\) , \( -5136 a + 3033\bigr] \)
116964.3-d2	\( \bigl[a\) , \( a\) , \( a\) , \( 589 a - 277\) , \( 3514 a + 1359\bigr] \)
116964.3-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 153 a + 48\) , \( -411 a + 1073\bigr] \)
116964.3-d4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 72 a + 23\) , \( 159 a - 434\bigr] \)
116964.3-d5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -63 a - 20\) , \( 84 a - 194\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph