Elliptic curve isogeny class 27.1-g over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-27.1-g
• Conductor: 27.1
• Rank bounds: 0...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-g over 4.4.9909.1

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

Curve label	Weierstrass Coefficients
27.1-g1	\( \bigl[a^{3} - 5 a - 2\) , \( a - 1\) , \( a + 1\) , \( -150 a^{3} + 183 a^{2} + 680 a - 380\) , \( -1452 a^{3} + 1764 a^{2} + 6589 a - 3657\bigr] \)
27.1-g2	\( \bigl[a^{3} - 5 a - 2\) , \( a - 1\) , \( a + 1\) , \( -2 a^{2} + 10\) , \( -9 a^{3} + 10 a^{2} + 41 a - 20\bigr] \)
27.1-g3	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 6 a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -53 a^{3} + 92 a^{2} + 122 a - 74\) , \( -182 a^{3} + 359 a^{2} + 449 a - 299\bigr] \)

Rank

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

Isogeny matrix

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

Isogeny graph