Elliptic curve isogeny class 28.3-a over number field 4.4.8768.1

• Base field: 4.4.8768.1
• Label: 4.4.8768.1-28.3-a
• Conductor: 28.3
• 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 28.3-a over 4.4.8768.1

Isogeny class 28.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
28.3-a1	\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - 6 a - 4\) , \( a^{3} - 5 a - 2\) , \( -5 a^{3} - 3 a^{2} + 14 a + 10\) , \( -20 a^{3} - 14 a^{2} + 63 a + 51\bigr] \)
28.3-a2	\( \bigl[a\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a^{3} - 5 a - 2\) , \( -12 a^{3} - 12 a^{2} + 37 a + 43\) , \( -81 a^{3} - 71 a^{2} + 250 a + 239\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph