Elliptic curve isogeny class 59.2-a over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-59.2-a
• Conductor: 59.2
• Rank: \( 1 \)

Base field 4.4.5725.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 11 \); class number \(1\).

Elliptic curves in class 59.2-a over 4.4.5725.1

Isogeny class 59.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
59.2-a1	\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -2 a^{2} + 2 a + 5\) , \( \frac{4}{3} a^{3} - 5 a^{2} + \frac{4}{3} a + \frac{19}{3}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph