Elliptic curve isogeny class 61731.3-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.3-g
• Conductor: 61731.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 61731.3-g over \(\Q(\sqrt{-3}) \)

Isogeny class 61731.3-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
61731.3-g1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 238 a - 817\) , \( 3795 a - 8972\bigr] \)
61731.3-g2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -42 a - 2\) , \( 343 a - 394\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph