Elliptic curve isogeny class 51.1-a over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-51.1-a
• Conductor: 51.1
• Rank: \( 2 \)

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 51.1-a over 4.4.19821.1

Isogeny class 51.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
51.1-a1	\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 3 a + 2\) , \( 0\) , \( \frac{4}{3} a^{3} - \frac{5}{3} a^{2} - 8 a + 10\) , \( -\frac{10}{3} a^{3} + \frac{41}{3} a^{2} - 13 a + 2\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph