Elliptic curve isogeny class 18900.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-18900.2-b
• Conductor: 18900.2
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 9 & 3 & 9 \\ 9 & 1 & 9 & 3 & 9 \\ 9 & 9 & 1 & 3 & 9 \\ 3 & 3 & 3 & 1 & 3 \\ 9 & 9 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 18900.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 18900.2-b contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
18900.2-b1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -196 a - 202\) , \( -1932 a - 872\bigr] \)
18900.2-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -15501 a + 1878\) , \( 776928 a - 505527\bigr] \)
18900.2-b3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1914 a + 2238\) , \( -56652 a + 106284\bigr] \)
18900.2-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -261 a - 162\) , \( -1032 a - 1671\bigr] \)
18900.2-b5	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 7539 a - 1362\) , \( -60792 a - 184191\bigr] \)