Elliptic curve isogeny class 49152.1-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-49152.1-e
• Conductor: 49152.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 49152.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 49152.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
49152.1-e1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 8\) , \( 8 a - 3\bigr] \)
49152.1-e2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 2\) , \( 2 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph