Elliptic curve isogeny class 36992.2-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36992.2-d
• Number of curves: 4
• Conductor: 36992.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 36992.2-d over \(\Q(\sqrt{-7}) \)

Isogeny class 36992.2-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36992.2-d1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -15 a - 6\) , \( 17 a - 6\bigr] \)
36992.2-d2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -565 a - 226\) , \( -5593 a + 1974\bigr] \)
36992.2-d3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -215 a - 86\) , \( 1785 a - 630\bigr] \)
36992.2-d4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -515 a - 206\) , \( -6987 a + 2466\bigr] \)