Elliptic curve isogeny class 36300.1-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36300.1-e
• Conductor: 36300.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 36300.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 36300.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
36300.1-e1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -5 a\) , \( 17\bigr] \)
36300.1-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -495 a\) , \( -7473\bigr] \)
36300.1-e3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 255 a\) , \( -1323\bigr] \)
36300.1-e4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 75 a\) , \( 225\bigr] \)
36300.1-e5	\( \bigl[a\) , \( 0\) , \( 0\) , \( 3885 a\) , \( -93525\bigr] \)
36300.1-e6	\( \bigl[a\) , \( 0\) , \( 0\) , \( 1175 a\) , \( 15405\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph