Elliptic curve isogeny class 17.1-a over number field 4.4.13068.1

• Base field: 4.4.13068.1
• Label: 4.4.13068.1-17.1-a
• Conductor: 17.1
• Rank: \( 2 \)

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-a over 4.4.13068.1

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

Curve label	Weierstrass Coefficients
17.1-a1	\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{2} - a - 3\) , \( -a^{2} + 2\) , \( 4 a^{2} + 7 a - 1\bigr] \)
17.1-a2	\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a\) , \( -a^{3} + 3 a^{2} - a - 1\) , \( -15 a^{3} + 42 a^{2} + 13 a - 8\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph