Elliptic curve isogeny class 36864.1-l over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36864.1-l
• Conductor: 36864.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 36864.1-l over \(\Q(\sqrt{-3}) \)

Isogeny class 36864.1-l contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
36864.1-l1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -67 a + 128\) , \( 346 a + 227\bigr] \)
36864.1-l2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -127 a + 68\) , \( 286 a - 445\bigr] \)
36864.1-l3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -187 a + 188\) , \( -8450 a + 4319\bigr] \)
36864.1-l4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7 a + 8\) , \( 10 a - 1\bigr] \)
36864.1-l5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 53 a - 52\) , \( 142 a - 97\bigr] \)
36864.1-l6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 293 a - 292\) , \( -2018 a + 863\bigr] \)
36864.1-l7	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 773 a - 772\) , \( 9790 a - 5281\bigr] \)
36864.1-l8	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4613 a - 4612\) , \( -137666 a + 66527\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\ 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph