Properties

Base field 4.4.8768.1
Label 4.4.8768.1-28.1-b
Conductor 28.1
Rank \( 0 \)

Related objects

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Base field 4.4.8768.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7 \); class number \(1\).

Elliptic curves in class 28.1-b over 4.4.8768.1

Isogeny class 28.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
28.1-b1 \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 2 a^{2} - 1\) , \( -27 a^{3} + 97 a^{2} - 27 a - 112\bigr] \)
28.1-b2 \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 4 a^{3} - 18 a^{2} + 10 a + 19\) , \( 714 a^{3} - 2617 a^{2} + 775 a + 3011\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph