Elliptic curve isogeny class 1648.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-1648.1-a
• Number of curves: 2
• Conductor: 1648.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1648.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 1648.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1648.1-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a + 1\) , \( 7 a - 6\bigr] \)
1648.1-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -126 a + 41\) , \( -433 a + 402\bigr] \)