Elliptic curve isogeny class 28224.6-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28224.6-a
• Conductor: 28224.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 28224.6-a over \(\Q(\sqrt{-7}) \)

Isogeny class 28224.6-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28224.6-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4 a - 79\) , \( 33 a + 303\bigr] \)
28224.6-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -114 a + 63\) , \( 45 a - 459\bigr] \)
28224.6-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 26 a - 7\) , \( 17 a - 53\bigr] \)
28224.6-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 341 a - 7\) , \( -739 a - 3455\bigr] \)

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