Elliptic curve isogeny class 8064.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-8064.2-a
• Conductor: 8064.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 8064.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 8064.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
8064.2-a1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -57 a + 4\) , \( 205 a - 119\bigr] \)
8064.2-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -38 a - 40\) , \( 196 a + 56\bigr] \)
8064.2-a3	\( \bigl[a\) , \( a\) , \( 0\) , \( -20 a - 9\) , \( 108 a - 23\bigr] \)
8064.2-a4	\( \bigl[a\) , \( a\) , \( 0\) , \( 1930 a + 771\) , \( 19782 a - 8435\bigr] \)
8064.2-a5	\( \bigl[a\) , \( a\) , \( 0\) , \( -520 a - 209\) , \( 2240 a - 399\bigr] \)
8064.2-a6	\( \bigl[a\) , \( a\) , \( 0\) , \( -4570 a - 1829\) , \( -180982 a + 67317\bigr] \)
8064.2-a7	\( \bigl[a\) , \( a\) , \( 0\) , \( -420 a - 169\) , \( 4860 a - 1399\bigr] \)
8064.2-a8	\( \bigl[a\) , \( a\) , \( 0\) , \( -6720 a - 2689\) , \( 319608 a - 107743\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 16 & 8 & 16 & 4 & 8 \\ 4 & 1 & 2 & 16 & 8 & 16 & 4 & 8 \\ 2 & 2 & 1 & 8 & 4 & 8 & 2 & 4 \\ 16 & 16 & 8 & 1 & 2 & 4 & 4 & 8 \\ 8 & 8 & 4 & 2 & 1 & 2 & 2 & 4 \\ 16 & 16 & 8 & 4 & 2 & 1 & 4 & 8 \\ 4 & 4 & 2 & 4 & 2 & 4 & 1 & 2 \\ 8 & 8 & 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph