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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20736.1-f
• Conductor: 20736.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
20736.1-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1461 a + 480\) , \( -18144 a + 17498\bigr] \)
20736.1-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -981 a - 480\) , \( 18144 a - 646\bigr] \)
20736.1-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 51 a\) , \( -142\bigr] \)
20736.1-f4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 219 a\) , \( -1654\bigr] \)
20736.1-f5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -21 a\) , \( 26\bigr] \)

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