Elliptic curve isogeny class 28.2-b over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-28.2-b
• Conductor: 28.2
• 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 \(1\).

Elliptic curves in class 28.2-b over 4.4.2624.1

Isogeny class 28.2-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
28.2-b1	\( \bigl[a^{2} - 2 a - 1\) , \( 0\) , \( 1\) , \( 100 a^{3} - 415 a^{2} + 240 a - 105\) , \( 1898 a^{3} - 6962 a^{2} + 2954 a + 534\bigr] \)
28.2-b2	\( \bigl[a^{2} - 2 a - 1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
28.2-b3	\( \bigl[a^{2} - 2 a - 1\) , \( 0\) , \( 1\) , \( -5 a^{2} + 10 a + 5\) , \( 2 a^{3} - 10 a^{2} + 10 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph