Elliptic curve isogeny class 17.4-b over number field 4.4.17069.1

• Base field: 4.4.17069.1
• Label: 4.4.17069.1-17.4-b
• Conductor: 17.4
• 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 17.4-b over 4.4.17069.1

Isogeny class 17.4-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
17.4-b1	\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( a + 1\) , \( -7 a^{3} + 8 a^{2} + 60 a + 49\) , \( -9 a^{3} + 10 a^{2} + 87 a + 75\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph