Properties

Base field 4.4.16357.1
Label 4.4.16357.1-25.2-g
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-g over 4.4.16357.1

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

Curve label Weierstrass Coefficients
25.2-g1 \( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 5 a\) , \( 1\) , \( -9 a^{3} + 5 a^{2} + 61 a - 11\) , \( -14 a^{3} + 11 a^{2} + 91 a - 38\bigr] \)
25.2-g2 \( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 5 a\) , \( 1\) , \( a^{3} + a + 14\) , \( a^{3} + 2 a^{2} + 2 a + 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph