Elliptic curve isogeny class 8064.5-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-8064.5-c
• Conductor: 8064.5
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 8064.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 8064.5-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
8064.5-c1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -93 a + 15\) , \( -414 a + 414\bigr] \)
8064.5-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -128 a + 112\) , \( -220 a + 948\bigr] \)
8064.5-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 a - 8\) , \( 20 a + 36\bigr] \)
8064.5-c4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 34\) , \( -14 a + 56\bigr] \)
8064.5-c5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 65 a - 134\) , \( 394 a - 512\bigr] \)
8064.5-c6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 49 a - 70\) , \( 190 a - 84\bigr] \)