Properties

Base field 4.4.17609.1
Label 4.4.17609.1-2.1-b
Conductor 2.1
Rank \( 1 \)

Related objects

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Base field 4.4.17609.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 10 x - 1 \); class number \(1\).

Elliptic curves in class 2.1-b over 4.4.17609.1

Isogeny class 2.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
2.1-b1 \( \bigl[a\) , \( -a^{2} - 2 a + 5\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 15 a^{3} + 6 a^{2} - 97 a + 18\) , \( 26 a^{3} + 12 a^{2} - 165 a + 21\bigr] \)
2.1-b2 \( \bigl[a^{3} - 6 a + 4\) , \( a^{3} + a^{2} - 5 a\) , \( a^{3} - 5 a + 3\) , \( -8 a^{3} + 9 a^{2} + 60 a - 83\) , \( -26 a^{3} + 24 a^{2} + 187 a - 246\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph