Elliptic curve isogeny class 39200.5-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39200.5-a
• Conductor: 39200.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 39200.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 39200.5-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
39200.5-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 99 a - 257\) , \( -849 a + 1295\bigr] \)
39200.5-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 57 a + 205\) , \( 1083 a - 1141\bigr] \)
39200.5-a3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -48 a + 16\) , \( -156 a - 168\bigr] \)
39200.5-a4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 372 a - 124\) , \( -1304 a - 2324\bigr] \)
39200.5-a5	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1842 a - 614\) , \( 19374 a + 25802\bigr] \)
39200.5-a6	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 5622 a - 1874\) , \( -103854 a - 156674\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph