Elliptic curve isogeny class 17.1-b over number field 4.4.6809.1

• Base field: 4.4.6809.1
• Label: 4.4.6809.1-17.1-b
• Conductor: 17.1
• Rank: \( 0 \)

Base field 4.4.6809.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 17.1-b over 4.4.6809.1

Isogeny class 17.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
17.1-b1	\( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 6 a + 3\) , \( a^{2} + a - 3\) , \( 16 a^{3} + 2 a^{2} - 77 a - 24\) , \( 67 a^{3} + 21 a^{2} - 325 a - 169\bigr] \)
17.1-b2	\( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 6 a + 3\) , \( a^{2} + a - 3\) , \( -4 a^{3} + 2 a^{2} + 18 a + 1\) , \( 3 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph