Elliptic curve isogeny class 36288.4-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36288.4-d
• Conductor: 36288.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 36288.4-d over \(\Q(\sqrt{-7}) \)

Isogeny class 36288.4-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
36288.4-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 27 a + 36\) , \( 81 a - 189\bigr] \)
36288.4-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( -54\bigr] \)
36288.4-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -531\) , \( 3726\bigr] \)
36288.4-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -171\) , \( -810\bigr] \)
36288.4-d5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -27 a + 63\) , \( -81 a - 108\bigr] \)
36288.4-d6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2691\) , \( -53730\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph