Elliptic curve isogeny class 15488.20-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15488.20-c
• Conductor: 15488.20
• Rank: \( 0 \)

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

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

Elliptic curves in class 15488.20-c over \(\Q(\sqrt{-7}) \)

Isogeny class 15488.20-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
15488.20-c1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 209\) , \( 128 a - 3204\bigr] \)
15488.20-c2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -148 a - 29\) , \( -567 a - 2768\bigr] \)
15488.20-c3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -92 a + 619\) , \( -3344 a + 181\bigr] \)
15488.20-c4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -437 a + 119\) , \( 3199 a - 3493\bigr] \)
15488.20-c5	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1372 a + 9579\) , \( -237584 a + 17845\bigr] \)
15488.20-c6	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6757 a + 1799\) , \( 217839 a - 268149\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph