Elliptic curve isogeny class 27.1-b over number field 4.4.11661.1

• Base field: 4.4.11661.1
• Label: 4.4.11661.1-27.1-b
• Conductor: 27.1
• Rank: \( 0 \)

Base field 4.4.11661.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 3 \); class number \(1\).

Elliptic curves in class 27.1-b over 4.4.11661.1

Isogeny class 27.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( 0\) , \( -3 a^{3} + 9 a^{2} + 7 a - 20\) , \( -27 a^{3} + 68 a^{2} + 75 a - 174\bigr] \)
27.1-b2	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 6 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -3 a^{2} + 6 a\) , \( 4 a^{3} - 16 a^{2} + 10 a + 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph