Properties

Base field 4.4.16357.1
Label 4.4.16357.1-25.2-b
Conductor 25.2
Rank \( 1 \)

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Base field 4.4.16357.1

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

Elliptic curves in class 25.2-b over 4.4.16357.1

Isogeny class 25.2-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
25.2-b1 \( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -6 a^{2} + 14 a - 1\) , \( -15 a^{3} + 33 a^{2} + 13 a - 7\bigr] \)
25.2-b2 \( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -a^{2} - a + 4\) , \( -2 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph