Elliptic curve isogeny class 64.2-e over number field 5.5.195829.1

• Base field: 5.5.195829.1
• Label: 5.5.195829.1-64.2-e
• Conductor: 64.2
• Rank: \( 1 \)

Base field 5.5.195829.1

Generator \(a\), with minimal polynomial \( x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 64.2-e over 5.5.195829.1

Isogeny class 64.2-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
64.2-e1	\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 10 a + 4\) , \( a^{3} - 4 a - 1\) , \( -7 a^{4} + 10 a^{3} + 28 a^{2} - 16 a\) , \( -21 a^{4} - 5 a^{3} + 112 a^{2} + 112 a + 17\bigr] \)
64.2-e2	\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 10 a + 4\) , \( a^{3} - 4 a - 1\) , \( 78 a^{4} - 140 a^{3} - 302 a^{2} + 314 a + 65\) , \( 257 a^{4} + 892 a^{3} - 2011 a^{2} - 5234 a - 833\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph