Properties

Base field 4.4.16357.1
Label 4.4.16357.1-25.2-a
Conductor 25.2
Rank \( 0 \)

Related objects

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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-a over 4.4.16357.1

Isogeny class 25.2-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
25.2-a1 \( \bigl[a^{3} - 6 a - 1\) , \( a^{3} - a^{2} - 6 a + 2\) , \( a^{3} - 6 a - 1\) , \( -123 a^{3} - 42 a^{2} + 724 a + 375\) , \( -109 a^{3} - 39 a^{2} + 644 a + 332\bigr] \)
25.2-a2 \( \bigl[a^{3} - 6 a\) , \( a^{3} - 7 a\) , \( a^{2} + a - 2\) , \( 5 a^{3} + 2 a^{2} - 24 a + 1\) , \( a^{2} + 4 a + 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph