Elliptic curve isogeny class 59.2-a over number field 4.4.2225.1

• Base field: 4.4.2225.1
• Label: 4.4.2225.1-59.2-a
• Conductor: 59.2
• 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 59.2-a over 4.4.2225.1

Isogeny class 59.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
59.2-a1	\( \bigl[a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 2\) , \( a + 1\) , \( -a^{3} + a^{2} + a + 1\) , \( \frac{3}{2} a^{3} - \frac{9}{2} a^{2} - \frac{1}{2} a + 3\bigr] \)
59.2-a2	\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 1\) , \( a^{2} - a - 2\) , \( -a^{2} + 4\) , \( -11 a^{3} + 20 a^{2} + 39 a - 55\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph