Properties

Base field 4.4.8069.1
Label 4.4.8069.1-25.1-b
Conductor 25.1
Rank \( 0 \)

Related objects

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Base field 4.4.8069.1

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

Elliptic curves in class 25.1-b over 4.4.8069.1

Isogeny class 25.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
25.1-b1 \( \bigl[a^{2} - 3\) , \( a^{3} - 4 a + 1\) , \( a^{2} + a - 3\) , \( 28 a^{3} + 7 a^{2} - 132 a - 25\) , \( 82 a^{3} + 20 a^{2} - 387 a - 72\bigr] \)
25.1-b2 \( \bigl[a^{3} - 4 a + 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -42 a^{3} - 52 a^{2} + 99 a + 20\) , \( 228 a^{3} + 254 a^{2} - 600 a - 115\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph