Elliptic curve isogeny class 4.1-a over number field 4.4.17609.1

• Base field: 4.4.17609.1
• Label: 4.4.17609.1-4.1-a
• Conductor: 4.1
• Rank: \( 1 \)

Base field 4.4.17609.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 10 x - 1 \); class number \(1\).

Elliptic curves in class 4.1-a over 4.4.17609.1

Isogeny class 4.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a\) , \( 2 a^{3} + a^{2} - 10 a + 3\) , \( -6 a^{3} - 6 a^{2} + 29 a - 4\) , \( 11 a^{3} + 13 a^{2} - 47 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph