Elliptic curve isogeny class 17.2-a over number field 4.4.16317.1

• Base field: 4.4.16317.1
• Label: 4.4.16317.1-17.2-a
• Conductor: 17.2
• Rank: \( 0 \)

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 17.2-a over 4.4.16317.1

Isogeny class 17.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
17.2-a1	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 4 a - 1\) , \( a^{3} - 3 a^{2} - 5 a + 7\) , \( -2 a^{2} - 2 a + 2\bigr] \)
17.2-a2	\( \bigl[a + 1\) , \( 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -11 a^{3} + 23 a^{2} + 41 a - 57\) , \( 27 a^{3} - 58 a^{2} - 98 a + 149\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph