Properties

Base field 4.4.17600.1
Label 4.4.17600.1-25.1-m
Conductor 25.1
Rank \( 1 \)

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Base field 4.4.17600.1

Generator \(a\), with minimal polynomial \( x^{4} - 14 x^{2} + 44 \); class number \(1\).

Elliptic curves in class 25.1-m over 4.4.17600.1

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

Curve label Weierstrass Coefficients
25.1-m1 \( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 4\) , \( \frac{1}{2} a^{2} - 4\) , \( -2 a^{3} - \frac{5}{2} a^{2} + 17 a + 30\) , \( \frac{1}{2} a^{3} + 2 a^{2} - 5 a - 16\bigr] \)
25.1-m2 \( \bigl[a\) , \( -\frac{1}{2} a^{2} - a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( -a^{3} - \frac{3}{2} a^{2} + 15 a - 13\) , \( a^{3} - \frac{5}{2} a^{2} - 19 a + 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph