Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.2-b
Conductor 55.2
Rank \( 1 \)

Related objects

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Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 55.2-b over 4.4.5125.1

Isogeny class 55.2-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
55.2-b1 \( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - a + 1\) , \( a^{3} - 6 a^{2} + 2 a + 11\bigr] \)
55.2-b2 \( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( 16 a^{3} - 41 a^{2} - 21 a + 46\) , \( 66 a^{3} - 198 a^{2} - 52 a + 280\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph