Properties

Base field 4.4.16357.1
Label 4.4.16357.1-25.3-a
Conductor 25.3
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 25.3-a over 4.4.16357.1

Isogeny class 25.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
25.3-a1 \( \bigl[a^{2} - 3\) , \( -a^{3} + 7 a\) , \( a\) , \( 15 a^{3} - 37 a^{2} + 16 a - 40\) , \( 188 a^{3} - 382 a^{2} - 293 a + 187\bigr] \)
25.3-a2 \( \bigl[a^{2} - 3\) , \( -a^{3} + 7 a\) , \( a\) , \( -2 a^{2} + 6 a\) , \( 4 a^{3} - 4 a^{2} - 14 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph