Properties

Base field 4.4.13768.1
Label 4.4.13768.1-9.1-b
Conductor 9.1
Rank \( 1 \)

Related objects

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Base field 4.4.13768.1

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

Elliptic curves in class 9.1-b over 4.4.13768.1

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

Curve label Weierstrass Coefficients
9.1-b1 \( \bigl[a\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 5 a^{3} - 3 a^{2} - 22 a - 8\) , \( -46 a^{3} + 6 a^{2} + 238 a + 108\bigr] \)
9.1-b2 \( \bigl[a\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 4 a - 1\) , \( 3 a^{3} + 7 a^{2} - 2 a - 2\) , \( -129 a^{3} - 200 a^{2} + 140 a + 101\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph