Elliptic curve isogeny class 17.1-e over number field \(\Q(\sqrt{221}) \)

• Base field: \(\Q(\sqrt{221}) \)
• Label: 2.2.221.1-17.1-e
• Conductor: 17.1
• Rank bounds: 0...1

Base field \(\Q(\sqrt{221}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 55 \); class number \(2\).

Elliptic curves in class 17.1-e over \(\Q(\sqrt{221}) \)

Isogeny class 17.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
17.1-e1	\( \bigl[a\) , \( 1\) , \( a\) , \( 2 a + 46\) , \( 6 a + 110\bigr] \)
17.1-e2	\( \bigl[a\) , \( 1\) , \( a\) , \( 7 a - 4\) , \( 7 a + 51\bigr] \)
17.1-e3	\( \bigl[a\) , \( 1\) , \( a\) , \( 2 a + 41\) , \( 5 a + 86\bigr] \)
17.1-e4	\( \bigl[a\) , \( 1\) , \( a\) , \( -3 a + 6\) , \( -41 a - 235\bigr] \)

Rank

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

Isogeny matrix

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

Isogeny graph