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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36300.1-c
• Conductor: 36300.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
36300.1-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -5204 a + 5204\) , \( -857220\bigr] \)
36300.1-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 256 a - 256\) , \( 0\bigr] \)
36300.1-c3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1024 a + 1024\) , \( 1792\bigr] \)
36300.1-c4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -10704 a + 10704\) , \( -418320\bigr] \)
36300.1-c5	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -11824 a + 11824\) , \( 500752\bigr] \)
36300.1-c6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -171084 a + 171084\) , \( -27137628\bigr] \)

Rank

Rank: \( 0 \)

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