Properties

Base field 5.5.24217.1
Label 5.5.24217.1-29.1-b
Conductor 29.1
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 29.1-b over 5.5.24217.1

Isogeny class 29.1-b contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
29.1-b1 \( \bigl[a^{4} - 4 a^{2}\) , \( -3 a^{4} + 14 a^{2} + a - 4\) , \( 2 a^{4} - 9 a^{2} + 2\) , \( 262 a^{4} - 221 a^{3} - 1174 a^{2} + 730 a + 366\) , \( 3311 a^{4} - 2134 a^{3} - 14758 a^{2} + 6316 a + 3956\bigr] \)
29.1-b2 \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 6\) , \( 2 a^{4} - 9 a^{2} + 3\) , \( -a^{4} + 4 a^{2} - 1\) , \( -a^{2} - a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph