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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36864.7-c
• 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-c over \(\Q(\sqrt{-7}) \)

Isogeny class 36864.7-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36864.7-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 31\) , \( 33\bigr] \)
36864.7-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( 9\bigr] \)
36864.7-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \)
36864.7-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -129\) , \( 609\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph