Elliptic curve isogeny class 81225.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.3-b
• Conductor: 81225.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 81225.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.3-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
81225.3-b1	\( \bigl[0\) , \( 0\) , \( a\) , \( -15 a + 6\) , \( 17 a - 19\bigr] \)
81225.3-b2	\( \bigl[0\) , \( 0\) , \( a\) , \( 1185 a - 1044\) , \( 16460 a - 5878\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph