Elliptic curve isogeny class 36288.2-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36288.2-d
• Conductor: 36288.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 36288.2-d over \(\Q(\sqrt{-7}) \)

Isogeny class 36288.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36288.2-d1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 51 a - 729\) , \( -624 a + 7952\bigr] \)
36288.2-d2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1083 a + 1650\) , \( -4343 a - 28358\bigr] \)
36288.2-d3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -138 a + 75\) , \( -689 a + 244\bigr] \)
36288.2-d4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 672 a - 735\) , \( -7331 a + 5590\bigr] \)