Properties

Base field 4.4.10025.1
Label 4.4.10025.1-20.4-b
Conductor 20.4
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 20.4-b over 4.4.10025.1

Isogeny class 20.4-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
20.4-b1 \( \bigl[a^{3} + 2 a^{2} - 7 a - 10\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( a + 1\) , \( -\frac{45}{2} a^{3} - \frac{425}{2} a^{2} + \frac{773}{2} a + 610\) , \( -1084 a^{3} + 1100 a^{2} + 3210 a + 929\bigr] \)
20.4-b2 \( \bigl[a^{3} + 2 a^{2} - 7 a - 10\) , \( a^{2} - a - 6\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( 43 a^{3} + 71 a^{2} - 292 a - 331\) , \( \frac{83}{2} a^{3} + \frac{215}{2} a^{2} - \frac{249}{2} a - 202\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph