Elliptic curve isogeny class 81225.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.1-b
• Conductor: 81225.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 81225.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.1-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
81225.1-b1	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -6 a + 15\) , \( -18 a - 2\bigr] \)
81225.1-b2	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 1044 a - 1185\) , \( -16461 a + 10582\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph