Elliptic curve isogeny class 13.1-a over number field 4.4.13968.1

• Base field: 4.4.13968.1
• Label: 4.4.13968.1-13.1-a
• Conductor: 13.1
• 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 13.1-a over 4.4.13968.1

Isogeny class 13.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
13.1-a1	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -a^{3} - a^{2} + 13 a - 7\) , \( -\frac{3}{2} a^{3} + \frac{15}{2} a^{2} - 17 a + 17\bigr] \)
13.1-a2	\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( 1\) , \( -4 a^{3} + 2 a^{2} + 33 a + 13\) , \( 13 a^{3} - \frac{17}{2} a^{2} - \frac{205}{2} a - 30\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph