Elliptic curve isogeny class 36864.7-l over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36864.7-l
• Conductor: 36864.7
• Rank: \( 2 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 36864.7-l over \(\Q(\sqrt{-7}) \)

Isogeny class 36864.7-l contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
36864.7-l1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 63\) , \( -1377\bigr] \)
36864.7-l2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \)
36864.7-l3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -17\) , \( 15\bigr] \)
36864.7-l4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -97\) , \( -385\bigr] \)
36864.7-l5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -257\) , \( 1503\bigr] \)
36864.7-l6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1537\) , \( -23713\bigr] \)

Rank

Rank: \( 2 \)

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