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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-288.5-a
• Conductor: 288.5
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

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

Isogeny class 288.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
288.5-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -2 a - 2\) , \( -2 a + 2\bigr] \)
288.5-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
288.5-a3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -12 a - 12\) , \( 14 a + 18\bigr] \)
288.5-a4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a - 8\) , \( -4 a + 2\bigr] \)