Properties

Base field 4.4.5125.1
Label 4.4.5125.1-55.1-b
Conductor 55.1
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 55.1-b over 4.4.5125.1

Isogeny class 55.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
55.1-b1 \( \bigl[a^{2} - a - 4\) , \( a^{3} - 4 a - 3\) , \( a^{2} - a - 4\) , \( a^{3} - 4 a - 2\) , \( -2 a^{3} + a^{2} + 7 a - 1\bigr] \)
55.1-b2 \( \bigl[a^{2} - a - 4\) , \( a^{3} - 4 a - 3\) , \( a^{2} - a - 4\) , \( -14 a^{3} + 5 a^{2} + 51 a - 2\) , \( -82 a^{3} - 21 a^{2} + 320 a + 197\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph