Properties

Base field 4.4.17428.1
Label 4.4.17428.1-9.1-b
Conductor 9.1
Rank \( 0 \)

Related objects

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Base field 4.4.17428.1

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

Elliptic curves in class 9.1-b over 4.4.17428.1

Isogeny class 9.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
9.1-b1 \( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 4 a - 1\) , \( -5 a^{3} + 16 a^{2} + 18 a - 54\) , \( -32 a^{3} + 62 a^{2} + 150 a - 266\bigr] \)
9.1-b2 \( \bigl[a\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{3} - 4 a - 1\) , \( -14 a^{3} + 8 a^{2} + 120 a - 144\) , \( -131 a^{3} + 274 a^{2} + 446 a - 854\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph