Elliptic curve isogeny class 27.1-e over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-27.1-e
• 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-e over 4.4.9909.1

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

Curve label	Weierstrass Coefficients
27.1-e1	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 6 a - 3\) , \( a\) , \( -97 a^{3} + 117 a^{2} + 438 a - 240\) , \( 696 a^{3} - 813 a^{2} - 3120 a + 1709\bigr] \)
27.1-e2	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 6 a - 3\) , \( a\) , \( -2 a^{3} + 2 a^{2} + 8 a\) , \( -a^{2} - 2 a\bigr] \)
27.1-e3	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 6 a - 3\) , \( a\) , \( -2 a^{3} - 33 a^{2} - 42 a + 30\) , \( -61 a^{3} - 168 a^{2} - 57 a + 80\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph