Elliptic curve isogeny class 232.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-232.4-a
• Conductor: 232.4
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 232.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 232.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
232.4-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4 a + 10\) , \( -14 a + 24\bigr] \)
232.4-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -21 a + 45\) , \( 33 a + 99\bigr] \)
232.4-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -a\) , \( 0\bigr] \)
232.4-a4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -6 a - 5\) , \( 11 a - 1\bigr] \)