Elliptic curve isogeny class 49.2-b over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-49.2-b
• Conductor: 49.2
• Rank: \( 1 \)

Base field 4.4.4205.1

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

Elliptic curves in class 49.2-b over 4.4.4205.1

Isogeny class 49.2-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
49.2-b1	\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( a + 1\) , \( 4 a^{3} - 7 a^{2} - 11 a\) , \( -7 a^{3} + 17 a^{2} + 8 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph