Elliptic curve isogeny class 161.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-161.1-a
• Conductor: 161.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 161.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 161.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
161.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a - 1\) , \( 0\bigr] \)
161.1-a2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -59 a + 69\) , \( -2 a + 254\bigr] \)
161.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -9 a + 9\) , \( 8 a - 31\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph