Elliptic curve isogeny class 123201.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-123201.1-a
• Conductor: 123201.1
• 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 123201.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 123201.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
123201.1-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -80 a + 272\) , \( 1451 a - 104\bigr] \)
123201.1-a2	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 50 a + 59\) , \( 249 a - 397\bigr] \)