Elliptic curve isogeny class 184.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-184.4-a
• Conductor: 184.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 184.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 184.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
184.4-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2\) , \( 0\bigr] \)
184.4-a2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( a + 1\) , \( a - 1\bigr] \)
184.4-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5 a - 8\) , \( 4\bigr] \)
184.4-a4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 26 a - 29\) , \( 69 a - 49\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph