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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-49152.1-r
• 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-r over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
49152.1-r1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 19 a - 15\) , \( 20 a - 5\bigr] \)
49152.1-r2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 9 a - 5\) , \( -8 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph