Elliptic curve isogeny class 9072.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9072.5-b
• Conductor: 9072.5
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 9072.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 9072.5-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9072.5-b1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -27 a - 270\) , \( 187 a + 1639\bigr] \)
9072.5-b2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 117 a - 423\) , \( -1350 a + 3078\bigr] \)
9072.5-b3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -18 a - 18\) , \( -135 a + 81\bigr] \)
9072.5-b4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -54 a + 30\) , \( -151 a + 249\bigr] \)
9072.5-b5	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -189 a + 255\) , \( -304 a - 1596\bigr] \)
9072.5-b6	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -90 a + 174\) , \( -295 a - 575\bigr] \)