LMFDB - Elliptic curve isogeny class 61.2-a over number field 5.5.24217.1

Base field 5.5.24217.1

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

Isogeny class 61.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
61.2-a1	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 3\) , \( 2 a^{4} - 10 a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( 4 a^{4} - 2 a^{3} - 20 a^{2} + 6 a + 9\) , \( 2 a^{4} - 4 a^{3} - 7 a^{2} + 9 a + 4\bigr] \)
61.2-a2	\( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{4} - 5 a^{2} + 3\) , \( -33 a^{4} + 86 a^{3} + 225 a^{2} - 86 a - 137\) , \( -317 a^{4} + 1250 a^{3} + 1079 a^{2} - 939 a - 684\bigr] \)

Rank: \( 0 \)

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

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