Elliptic curve isogeny class 17.2-a over number field 4.4.8069.1

• Base field: 4.4.8069.1
• Label: 4.4.8069.1-17.2-a
• Conductor: 17.2
• Rank: \( 0 \)

Base field 4.4.8069.1

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

Elliptic curves in class 17.2-a over 4.4.8069.1

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

Curve label	Weierstrass Coefficients
17.2-a1	\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 3\) , \( -6 a^{3} + 2 a^{2} + 30 a - 21\) , \( 13 a^{3} - 16 a^{2} - 44 a + 36\bigr] \)
17.2-a2	\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 3\) , \( -a^{3} + 2 a^{2} - 6\) , \( a^{2} - 3 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph