Elliptic curve isogeny class 13.2-b over number field 4.4.13968.1

• Base field: 4.4.13968.1
• Label: 4.4.13968.1-13.2-b
• Conductor: 13.2
• Rank: \( 1 \)

Base field 4.4.13968.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 4 \); class number \(1\).

Elliptic curves in class 13.2-b over 4.4.13968.1

Isogeny class 13.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
13.2-b1	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - a\) , \( -\frac{3}{2} a^{3} - 7 a^{2} - \frac{19}{2} a - 3\bigr] \)
13.2-b2	\( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{47}{2} a^{3} - \frac{61}{2} a^{2} + 67 a + 30\) , \( -\frac{461}{2} a^{3} - \frac{589}{2} a^{2} + 647 a + 281\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph