Elliptic curve isogeny class 28.2-a over number field 4.4.8768.1

• Base field: 4.4.8768.1
• Label: 4.4.8768.1-28.2-a
• Conductor: 28.2
• 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 28.2-a over 4.4.8768.1

Isogeny class 28.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
28.2-a1	\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 5 a - 2\) , \( -4 a^{2} + 5 a + 18\) , \( 2 a^{2} - a - 9\bigr] \)
28.2-a2	\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 5 a - 2\) , \( 10 a^{3} - 49 a^{2} + 35 a + 68\) , \( 57 a^{3} - 233 a^{2} + 119 a + 261\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph