Elliptic curve isogeny class 11.2-b over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-11.2-b
• Conductor: 11.2
• Rank: \( 0 \)

Base field 5.5.70601.1

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

Elliptic curves in class 11.2-b over 5.5.70601.1

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

Curve label	Weierstrass Coefficients
11.2-b1	\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 3\) , \( -a^{2} + 5\) , \( 2 a^{4} - 12 a^{2} - 4 a + 6\bigr] \)
11.2-b2	\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( a^{4} - a^{3} - 5 a^{2} + a + 2\) , \( a^{4} - 6 a^{2} - 2 a + 3\) , \( -28 a^{4} + 4 a^{3} + 105 a^{2} - 20 a - 66\) , \( -172 a^{4} - 86 a^{3} + 571 a^{2} + 100 a - 379\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph