Elliptic curve isogeny class 28.4-b over number field 4.4.8768.1

• Base field: 4.4.8768.1
• Label: 4.4.8768.1-28.4-b
• Conductor: 28.4
• Rank: \( 0 \)

Base field 4.4.8768.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7 \); class number \(1\).

Elliptic curves in class 28.4-b over 4.4.8768.1

Isogeny class 28.4-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
28.4-b1	\( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 4 a - 2\) , \( 0\) , \( 26 a^{3} + 17 a^{2} - 85 a - 69\bigr] \)
28.4-b2	\( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 4 a - 2\) , \( -5 a^{3} - 5 a^{2} + 15 a + 15\) , \( -715 a^{3} - 474 a^{2} + 2318 a + 1883\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph