Properties

Base field 5.5.138136.1
Label 5.5.138136.1-28.1-c
Conductor 28.1
Rank \( 0 \)

Related objects

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Base field 5.5.138136.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 4 x - 2 \); class number \(1\).

Elliptic curves in class 28.1-c over 5.5.138136.1

Isogeny class 28.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
28.1-c1 \( \bigl[3 a^{4} - a^{3} - 19 a^{2} - 2 a + 12\) , \( -2 a^{4} + a^{3} + 11 a^{2} + a - 4\) , \( 0\) , \( 67 a^{4} - 18 a^{3} - 412 a^{2} - 104 a + 177\) , \( 391 a^{4} - 88 a^{3} - 2408 a^{2} - 699 a + 990\bigr] \)
28.1-c2 \( \bigl[a^{4} - 7 a^{2} - a + 6\) , \( -2 a^{4} + 13 a^{2} + 6 a - 8\) , \( 2 a^{4} - a^{3} - 12 a^{2} + 6\) , \( 19 a^{4} - 4 a^{3} - 117 a^{2} - 37 a + 45\) , \( 103 a^{4} - 22 a^{3} - 635 a^{2} - 191 a + 260\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph