Elliptic curve isogeny class 768.5-i over number field \(\Q(\sqrt{-39}) \)

• Base field: \(\Q(\sqrt{-39}) \)
• Label: 2.0.39.1-768.5-i
• Conductor: 768.5
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-39}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 10 \); class number \(4\).

Elliptic curves in class 768.5-i over \(\Q(\sqrt{-39}) \)

Isogeny class 768.5-i contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
768.5-i1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -5460 a - 10924\) , \( -382436 a - 104400\bigr] \)
768.5-i2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -285 a - 929\) , \( -6324 a + 6048\bigr] \)
768.5-i3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2568 a - 10899\) , \( -181656 a - 7310\bigr] \)
768.5-i4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 60 a + 116\) , \( 124 a + 240\bigr] \)
768.5-i5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -260 a - 524\) , \( 1788 a - 528\bigr] \)
768.5-i6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -312 a + 1341\) , \( 3816 a + 17890\bigr] \)
768.5-i7	\( \bigl[0\) , \( -a\) , \( 0\) , \( 35 a + 111\) , \( 92 a - 688\bigr] \)
768.5-i8	\( \bigl[0\) , \( -a\) , \( 0\) , \( -87380 a - 174764\) , \( -24729060 a - 5806032\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 5 & 10 & 10 & 10 & 2 \\ 2 & 1 & 4 & 10 & 20 & 20 & 5 & 4 \\ 2 & 4 & 1 & 10 & 20 & 5 & 20 & 4 \\ 5 & 10 & 10 & 1 & 2 & 2 & 2 & 10 \\ 10 & 20 & 20 & 2 & 1 & 4 & 4 & 5 \\ 10 & 20 & 5 & 2 & 4 & 1 & 4 & 20 \\ 10 & 5 & 20 & 2 & 4 & 4 & 1 & 20 \\ 2 & 4 & 4 & 10 & 5 & 20 & 20 & 1 \end{array}\right)\)

Isogeny graph