Elliptic curve isogeny class 288.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-288.5-b
• Conductor: 288.5
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 288.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 288.5-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
288.5-b1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a\) , \( -6 a - 8\bigr] \)
288.5-b2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -a + 11\) , \( -3 a - 3\bigr] \)
288.5-b3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( a - 11\) , \( -3 a - 3\bigr] \)
288.5-b4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 59 a - 20\) , \( -106 a - 188\bigr] \)
288.5-b5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -14 a - 6\) , \( -28 a + 8\bigr] \)
288.5-b6	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -18 a + 15\) , \( 13 a - 31\bigr] \)
288.5-b7	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -224 a - 96\) , \( -1942 a + 614\bigr] \)
288.5-b8	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -258 a + 255\) , \( 589 a - 2623\bigr] \)