Elliptic curve isogeny class 20736.1-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20736.1-d
• Conductor: 20736.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 20736.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 20736.1-d contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
20736.1-d1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -159 a - 327\) , \( -1657 a - 2032\bigr] \)
20736.1-d2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 328 a + 160\) , \( -2144 a + 4016\bigr] \)
20736.1-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 153\) , \( -852 a + 426\bigr] \)
20736.1-d4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( 343 a - 208\bigr] \)
20736.1-d5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -63\) , \( 156 a - 78\bigr] \)

Rank

Rank: \( 0 \)

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