Elliptic curve isogeny class 18688.1-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-18688.1-e
• Conductor: 18688.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 18688.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 18688.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
18688.1-e1	\( \bigl[0\) , \( a\) , \( 0\) , \( -234 a + 77\) , \( 1113 a - 1050\bigr] \)
18688.1-e2	\( \bigl[0\) , \( a\) , \( 0\) , \( 86 a - 83\) , \( 345 a - 186\bigr] \)
18688.1-e3	\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 3\) , \( 9 a - 10\bigr] \)
18688.1-e4	\( \bigl[0\) , \( a\) , \( 0\) , \( -234 a + 157\) , \( 1849 a - 714\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph