Elliptic curve isogeny class 28.1-b over number field 5.5.138136.1

• Base field: 5.5.138136.1
• Label: 5.5.138136.1-28.1-b
• Conductor: 28.1
• Rank: \( 0 \)

Base field 5.5.138136.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 4 x - 2 \); class number \(1\).

Elliptic curves in class 28.1-b over 5.5.138136.1

Isogeny class 28.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
28.1-b1	\( \bigl[4 a^{4} - a^{3} - 25 a^{2} - 5 a + 14\) , \( a^{4} - 6 a^{2} - 4 a + 3\) , \( 2 a^{4} - a^{3} - 12 a^{2} + 6\) , \( -a^{3} + 5 a^{2} - 2 a - 3\) , \( -14 a^{4} + 4 a^{3} + 96 a^{2} + 6 a - 61\bigr] \)
28.1-b2	\( \bigl[3 a^{4} - a^{3} - 18 a^{2} - 4 a + 8\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 2 a - 5\) , \( 3 a^{4} - a^{3} - 19 a^{2} - 2 a + 12\) , \( 69 a^{4} - 14 a^{3} - 425 a^{2} - 132 a + 173\) , \( -2772 a^{4} + 592 a^{3} + 17097 a^{2} + 5130 a - 7051\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph