Elliptic curve isogeny class 11.2-a over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-11.2-a
• Conductor: 11.2
• Rank: \( 0 \)

Base field 5.5.38569.1

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

Elliptic curves in class 11.2-a over 5.5.38569.1

Isogeny class 11.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
11.2-a1	\( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 3\) , \( a^{3} - 4 a + 1\) , \( -a^{4} + 3 a^{2} + a + 2\) , \( a^{4} - 4 a^{2} - 1\bigr] \)
11.2-a2	\( \bigl[-a^{4} + 5 a^{2} + a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -6 a^{4} - 90 a^{3} + 108 a^{2} + 359 a - 308\) , \( 40 a^{4} - 663 a^{3} + 389 a^{2} + 2588 a - 1988\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph