Elliptic curve isogeny class 116964.1-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-116964.1-d
• Conductor: 116964.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 116964.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 116964.1-d contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
116964.1-d1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -588 a + 312\) , \( -3791 a + 5462\bigr] \)
116964.1-d2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -59 a + 538\) , \( 5135 a - 2103\bigr] \)
116964.1-d3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -48 a - 153\) , \( 411 a + 662\bigr] \)
116964.1-d4	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -24 a - 72\) , \( -160 a - 275\bigr] \)
116964.1-d5	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 19 a + 63\) , \( -84 a - 110\bigr] \)

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