Elliptic curve isogeny class 53.2-a over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-53.2-a
• Conductor: 53.2
• 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 53.2-a over 5.5.70601.1

Isogeny class 53.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
53.2-a1	\( \bigl[a + 1\) , \( -a^{4} + a^{3} + 4 a^{2}\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 2\) , \( -7 a^{4} + 3 a^{3} + 39 a^{2} + 5 a - 25\) , \( 9 a^{4} - 7 a^{3} - 46 a^{2} + 8 a + 25\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph