Elliptic curve isogeny class 13552.10-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-13552.10-c
• Conductor: 13552.10
• Rank: \( 0 \)

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

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

Elliptic curves in class 13552.10-c over \(\Q(\sqrt{-7}) \)

Isogeny class 13552.10-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
13552.10-c1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -663 a + 405\) , \( 4843 a - 10065\bigr] \)
13552.10-c2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 96 a + 22\) , \( 35 a + 616\bigr] \)
13552.10-c3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -43 a + 25\) , \( 83 a - 153\bigr] \)
13552.10-c4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 22 a + 111\) , \( -273 a + 575\bigr] \)
13552.10-c5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 16 a - 8\) , \( 48 a + 32\bigr] \)
13552.10-c6	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 12 a - 39\) , \( -81 a + 67\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph