Elliptic curve isogeny class 17.1-b over number field 4.4.13068.1

• Base field: 4.4.13068.1
• Label: 4.4.13068.1-17.1-b
• Conductor: 17.1
• Rank: \( 1 \)

Base field 4.4.13068.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 17.1-b over 4.4.13068.1

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

Curve label	Weierstrass Coefficients
17.1-b1	\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 7 a - 2\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{3} + 8 a + 8\) , \( 12 a^{3} - 9 a^{2} - 74 a - 37\bigr] \)
17.1-b2	\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( 0\) , \( -6 a^{3} + 9 a^{2} + 30 a - 4\) , \( -4 a^{3} + 6 a^{2} + 20 a - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph