Elliptic curve isogeny class 9.1-a over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-9.1-a
• Conductor: 9.1
• Rank bounds: 0...1

Base field 4.4.19821.1

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

Elliptic curves in class 9.1-a over 4.4.19821.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( 1899 a^{3} - 3107 a^{2} - 25597 a - 9911\) , \( 107727 a^{3} - 331234 a^{2} - 1894883 a - 638778\bigr] \)
9.1-a2	\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( -a^{3} + 3 a^{2} + 8 a + 4\) , \( 3 a^{3} + 8 a^{2} - 11 a - 3\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph