Elliptic curve isogeny class 57.1-b over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-57.1-b
• Conductor: 57.1
• Rank: \( 1 \)

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 57.1-b over 4.4.19821.1

Isogeny class 57.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
57.1-b1	\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( a\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( 2 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph