Properties

Base field 4.4.10025.1
Label 4.4.10025.1-20.3-a
Conductor 20.3
Rank \( 1 \)

Related objects

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Base field 4.4.10025.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 10 x + 20 \); class number \(1\).

Elliptic curves in class 20.3-a over 4.4.10025.1

Isogeny class 20.3-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
20.3-a1 \( \bigl[a^{3} + 2 a^{2} - 6 a - 11\) , \( -a\) , \( 1\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - \frac{21}{2} a - 8\) , \( 11 a^{3} - 16 a^{2} - 94 a + 165\bigr] \)
20.3-a2 \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( a^{2} + a - 4\) , \( 1\) , \( -2 a^{3} + 19 a^{2} + 20 a - 124\) , \( -15 a^{3} + 47 a^{2} + 148 a - 416\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph