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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36864.7-a
• Conductor: 36864.7
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

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

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

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

Curve label	Weierstrass Coefficients
36864.7-a1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -171 a - 183\) , \( -1719 a - 243\bigr] \)
36864.7-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a - 23\) , \( -23 a + 45\bigr] \)
36864.7-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( -21 a + 30\) , \( 9 a + 42\bigr] \)
36864.7-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -69 a + 46\) , \( -137 a + 310\bigr] \)