Elliptic curve isogeny class 28.1-b over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-28.1-b
• Number of curves: 3
• Conductor: 28.1
• Rank: \( 0 \)

Base field 4.4.2624.1

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 28.1-b over 4.4.2624.1

Isogeny class 28.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
28.1-b1	\( \bigl[a^{2} - 2 a\) , \( -a^{2} + 2 a + 1\) , \( 1\) , \( 110 a^{3} - 6 a^{2} - 658 a - 729\) , \( 2316 a^{3} - 1466 a^{2} - 11382 a - 8128\bigr] \)
28.1-b2	\( \bigl[a^{2} - 2 a\) , \( -a^{2} + 2 a + 1\) , \( 1\) , \( 4 a^{2} - 8 a - 9\) , \( 4 a^{3} - 2 a^{2} - 22 a - 16\bigr] \)
28.1-b3	\( \bigl[a^{2} - 2 a\) , \( -a^{2} + 2 a + 1\) , \( 1\) , \( -a^{2} + 2 a + 1\) , \( 0\bigr] \)