Elliptic curve isogeny class 17.3-b over number field 4.4.17069.1

• Base field: 4.4.17069.1
• Label: 4.4.17069.1-17.3-b
• Conductor: 17.3
• Rank: \( 1 \)

Base field 4.4.17069.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} - 4 x + 3 \); class number \(1\).

Elliptic curves in class 17.3-b over 4.4.17069.1

Isogeny class 17.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
17.3-b1	\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( a^{2} - a - 4\) , \( -a^{3} + 4 a^{2} + 12 a + 6\) , \( -a^{3} + 6 a^{2} + 18 a + 11\bigr] \)
17.3-b2	\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a + 1\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 278 a^{3} - 166 a^{2} - 2287 a - 2039\) , \( -5572 a^{3} + 3299 a^{2} + 45925 a + 41014\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph