Elliptic curve isogeny class 59.1-a over number field 4.4.2225.1

• Base field: 4.4.2225.1
• Label: 4.4.2225.1-59.1-a
• Conductor: 59.1
• Rank: \( 0 \)

Base field 4.4.2225.1

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

Elliptic curves in class 59.1-a over 4.4.2225.1

Isogeny class 59.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
59.1-a1	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( -a^{3} + 2 a^{2} - 1\) , \( a^{3} + 2 a^{2} - 8 a - 8\bigr] \)
59.1-a2	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -a^{2} + 2\) , \( a^{2} - a - 3\) , \( a^{2} - a - 1\) , \( -\frac{7}{2} a^{3} - \frac{11}{2} a^{2} + \frac{9}{2} a + 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph