Elliptic curve isogeny class 268.3-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-268.3-a
• Conductor: 268.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 268.3-a over \(\Q(\sqrt{-7}) \)

Isogeny class 268.3-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
268.3-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -9 a + 4\) , \( 5 a - 10\bigr] \)
268.3-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \)
268.3-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -209 a + 149\) , \( -797 a + 1955\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph