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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36864.1-p
• Conductor: 36864.1
• Rank: \( 0 \)

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

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

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

Isogeny class 36864.1-p contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36864.1-p1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 12\) , \( 0\bigr] \)
36864.1-p2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 0\bigr] \)
36864.1-p3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 132 a - 132\) , \( -672 a + 336\bigr] \)
36864.1-p4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 132 a - 132\) , \( 672 a - 336\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph