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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.3-d
• 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-d over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
81225.3-d1	\( \bigl[1\) , \( a\) , \( 1\) , \( -2 a - 1\) , \( 4 a - 7\bigr] \)
81225.3-d2	\( \bigl[1\) , \( a\) , \( 1\) , \( -77 a + 29\) , \( 184 a - 193\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph