Elliptic curve isogeny class 27.1-b over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-27.1-b
• Conductor: 27.1
• Rank: \( 1 \)

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 27.1-b over 4.4.9909.1

Isogeny class 27.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{3} - 4 a - 1\) , \( -2 a^{3} + a^{2} + 7 a - 4\) , \( -3 a^{3} + 3 a^{2} + 12 a - 8\bigr] \)
27.1-b2	\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{3} - 4 a - 1\) , \( 18 a^{3} - 29 a^{2} - 73 a + 41\) , \( -8 a^{3} + 24 a^{2} - 2 a - 6\bigr] \)
27.1-b3	\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a - 1\) , \( -a^{3} - 4 a^{2} - a - 2\) , \( -167 a^{3} - 442 a^{2} - 128 a + 194\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph