Elliptic curve isogeny class 136900.2-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-136900.2-d
• Conductor: 136900.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 136900.2-d over \(\Q(\sqrt{-3}) \)

Isogeny class 136900.2-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
136900.2-d1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 5255 a\) , \( -149075\bigr] \)
136900.2-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -245 a\) , \( -975\bigr] \)
136900.2-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 75 a\) , \( -143\bigr] \)
136900.2-d4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 5275 a\) , \( -147903\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph