Properties

Base field 5.5.24217.1
Label 5.5.24217.1-97.2-a
Conductor 97.2
Rank \( 0 \)

Related objects

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Base field 5.5.24217.1

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

Elliptic curves in class 97.2-a over 5.5.24217.1

Isogeny class 97.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
97.2-a1 \( \bigl[2 a^{4} - 9 a^{2} + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{2} + a - 2\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 7 a\) , \( -3 a^{4} + 14 a^{2} + a - 7\bigr] \)
97.2-a2 \( \bigl[2 a^{4} - 9 a^{2} + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{2} + a - 2\) , \( -31 a^{4} + 8 a^{3} + 149 a^{2} - 13 a - 80\) , \( -110 a^{4} + 39 a^{3} + 534 a^{2} - 81 a - 295\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph