Elliptic curve isogeny class 652.1-c over number field \(\Q(\sqrt{-163}) \)

• Base field: \(\Q(\sqrt{-163}) \)
• Label: 2.0.163.1-652.1-c
• Conductor: 652.1
• Rank bounds: 0...1

Base field \(\Q(\sqrt{-163}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 41 \); class number \(1\).

Elliptic curves in class 652.1-c over \(\Q(\sqrt{-163}) \)

Isogeny class 652.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
652.1-c1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -355\) , \( 1182\bigr] \)
652.1-c2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -14210\) , \( -653100\bigr] \)
652.1-c3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -300\) , \( 1970\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph