Elliptic curve isogeny class 9.2-a over number field 4.4.10309.1

• Base field: 4.4.10309.1
• Label: 4.4.10309.1-9.2-a
• Number of curves: 2
• Conductor: 9.2
• Rank: \( 0 \)

Base field 4.4.10309.1

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 9.2-a over 4.4.10309.1

Isogeny class 9.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
9.2-a1	\( \bigl[0\) , \( -a^{2} - a + 4\) , \( a^{3} - 6 a + 4\) , \( 13 a^{3} - 47 a^{2} + 40 a - 5\) , \( 845 a^{3} - 3012 a^{2} + 2715 a - 335\bigr] \)
9.2-a2	\( \bigl[0\) , \( -a^{2} - a + 4\) , \( a^{3} - 6 a + 4\) , \( -a^{3} - a^{2} + 4 a - 1\) , \( 2 a^{3} + 3 a^{2} - 6 a - 2\bigr] \)