Elliptic curve isogeny class 17.1-b over number field 4.4.16317.1

• Base field: 4.4.16317.1
• Label: 4.4.16317.1-17.1-b
• Conductor: 17.1
• Rank: \( 1 \)

Base field 4.4.16317.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 17.1-b over 4.4.16317.1

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

Curve label	Weierstrass Coefficients
17.1-b1	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 6 a + 5\) , \( -3 a^{3} + 5 a^{2} + 10 a - 15\bigr] \)
17.1-b2	\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - 2\) , \( 2 a^{3} - 6 a^{2} + 2 a + 3\) , \( 6 a^{3} - 22 a^{2} + 14 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph