Elliptic curve isogeny class 268.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-268.4-a
• Conductor: 268.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 268.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 268.4-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
268.4-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 9 a - 5\) , \( -5 a - 5\bigr] \)
268.4-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -a\) , \( -a\bigr] \)
268.4-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 209 a - 60\) , \( 797 a + 1158\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph