Properties

Base field 4.4.9909.1
Label 4.4.9909.1-25.1-e
Conductor 25.1
Rank \( 1 \)

Related objects

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Base field 4.4.9909.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 3 x + 3 \); class number \(1\).

Elliptic curves in class 25.1-e over 4.4.9909.1

Isogeny class 25.1-e contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
25.1-e1 \( \bigl[0\) , \( -a^{3} + a^{2} + 3 a\) , \( a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( -5 a^{3} + 6 a^{2} + 21 a - 12\bigr] \)
25.1-e2 \( \bigl[0\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( -2 a^{3} + 4 a^{2} + 5 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph