Elliptic curve isogeny class 120000.1-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-120000.1-g
• Conductor: 120000.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 120000.1-g over \(\Q(\sqrt{-3}) \)

Isogeny class 120000.1-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
120000.1-g1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 792 a - 792\) , \( -6912\bigr] \)
120000.1-g2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -4208 a + 4208\) , \( -66912\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph