Elliptic curve isogeny class 17.1-c over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-17.1-c
• Conductor: 17.1
• Rank: \( 0 \)

Base field 4.4.5744.1

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

Elliptic curves in class 17.1-c over 4.4.5744.1

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

Curve label	Weierstrass Coefficients
17.1-c1	\( \bigl[-a^{3} + a^{2} + 4 a\) , \( a^{3} - 6 a - 1\) , \( a^{3} - 5 a - 1\) , \( 46 a^{3} - 207 a - 127\) , \( 207 a^{3} - 3 a^{2} - 915 a - 596\bigr] \)
17.1-c2	\( \bigl[-a^{3} + a^{2} + 4 a\) , \( a^{3} - 6 a - 1\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 7 a + 3\) , \( a^{2} - 2 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph