Elliptic curve isogeny class 18688.2-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-18688.2-e
• Conductor: 18688.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 18688.2-e over \(\Q(\sqrt{-3}) \)

Isogeny class 18688.2-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
18688.2-e1	\( \bigl[0\) , \( a\) , \( 0\) , \( -77 a + 234\) , \( -1113 a + 63\bigr] \)
18688.2-e2	\( \bigl[0\) , \( a\) , \( 0\) , \( 83 a - 86\) , \( -345 a + 159\bigr] \)
18688.2-e3	\( \bigl[0\) , \( a\) , \( 0\) , \( -157 a + 234\) , \( -1849 a + 1135\bigr] \)
18688.2-e4	\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 6\) , \( -9 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph