Elliptic curve isogeny class 27.1-a over number field 4.4.9909.1

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

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

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 10 a^{3} - 13 a^{2} - 29 a + 8\) , \( -22 a^{3} + 23 a^{2} + 42 a - 20\bigr] \)
27.1-a2	\( \bigl[a\) , \( 0\) , \( a^{2} - 2\) , \( -23 a^{3} + 27 a^{2} + 100 a - 54\) , \( -467 a^{3} + 562 a^{2} + 2118 a - 1159\bigr] \)
27.1-a3	\( \bigl[a\) , \( 0\) , \( a^{2} - 2\) , \( 2 a^{3} - 3 a^{2} - 10 a + 6\) , \( 17 a^{3} - 21 a^{2} - 78 a + 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph