Elliptic curve isogeny class 4032.1-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4032.1-c
• Conductor: 4032.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4032.1-c over \(\Q(\sqrt{-7}) \)

Isogeny class 4032.1-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
4032.1-c1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -170 a - 68\) , \( -3689 a + 1302\bigr] \)
4032.1-c2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 5 a + 2\) , \( 0\bigr] \)
4032.1-c3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -20 a - 8\) , \( -17 a + 6\bigr] \)
4032.1-c4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -195 a - 78\) , \( 1530 a - 540\bigr] \)
4032.1-c5	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 11 a - 20\) , \( -38 a + 27\bigr] \)
4032.1-c6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -6 a + 24\) , \( -21 a - 18\bigr] \)
4032.1-c7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -245 a - 98\) , \( -2312 a + 816\bigr] \)
4032.1-c8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -3920 a - 1568\) , \( -144755 a + 51090\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph