Elliptic curve isogeny class 108300.2-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-108300.2-g
• Conductor: 108300.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 108300.2-g over \(\Q(\sqrt{-3}) \)

Isogeny class 108300.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
108300.2-g1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 12 a - 13\) , \( -14\bigr] \)
108300.2-g2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -68 a + 67\) , \( -142\bigr] \)
108300.2-g3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -448 a + 447\) , \( 3506\bigr] \)
108300.2-g4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -968 a + 967\) , \( -11662\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph