Elliptic curve isogeny class 85.2-a over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-85.2-a
• Conductor: 85.2
• Rank: \( 0 \)

Base field 5.5.24217.1

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

Elliptic curves in class 85.2-a over 5.5.24217.1

Isogeny class 85.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
85.2-a1	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 5 a + 7\) , \( 0\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 3 a + 6\) , \( 0\bigr] \)
85.2-a2	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 5 a + 7\) , \( 0\) , \( -8 a^{4} + 4 a^{3} + 36 a^{2} - 12 a - 24\) , \( -34 a^{4} + 13 a^{3} + 154 a^{2} - 33 a - 90\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph