Properties

Base field 4.4.9909.1
Label 4.4.9909.1-25.1-d
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-d over 4.4.9909.1

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

Curve label Weierstrass Coefficients
25.1-d1 \( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - a - 3\) , \( -5 a^{3} + 3 a^{2} + 25 a + 4\) , \( 5 a^{3} - 10 a^{2} - 19 a + 31\bigr] \)
25.1-d2 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 2 a^{3} + 4 a^{2} - 6 a - 13\) , \( 2 a^{3} + 7 a^{2} - 6 a - 23\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph