Elliptic Curve Isogeny Class 13.1-b over Number Field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-13.1-b
• Conductor: 13.1
• Rank: not recorded

Base field 4.4.9909.1

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

Elliptic curves in class 13.1-b over 4.4.9909.1

Isogeny class 13.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
13.1-b1	\( \bigl[a^{3} - 4 a - 2\) , \( a\) , \( a^{3} - 5 a - 1\) , \( 9 a^{3} - 18 a^{2} - 22 a + 14\) , \( -46 a^{3} + 74 a^{2} + 104 a - 66\bigr] \)
13.1-b2	\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 5 a\) , \( a^{2} - a - 2\) , \( -130 a^{3} + 234 a^{2} + 353 a - 228\) , \( 477 a^{3} - 959 a^{2} - 995 a + 687\bigr] \)
13.1-b3	\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a\) , \( 1\) , \( -220 a^{3} + 274 a^{2} + 1002 a - 570\) , \( 2785 a^{3} - 3453 a^{2} - 12765 a + 7022\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph