Elliptic curve isogeny class 53.1-a over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-53.1-a
• Conductor: 53.1
• Rank: \( 1 \)

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 53.1-a over 5.5.70601.1

Isogeny class 53.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
53.1-a1	\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 3\) , \( 30 a^{4} - 5 a^{3} - 157 a^{2} - 65 a + 36\) , \( 142 a^{4} - 64 a^{3} - 658 a^{2} - 250 a + 149\bigr] \)
53.1-a2	\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( a^{4} + 6 a^{3} - 11 a^{2} - 29 a + 7\) , \( 7 a^{4} + 2 a^{3} - 39 a^{2} - 30 a + 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph