Properties

Base field 4.4.17600.1
Label 4.4.17600.1-25.1-h
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-h over 4.4.17600.1

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

Curve label Weierstrass Coefficients
25.1-h1 \( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( \frac{1}{2} a^{2} - 4\) , \( \frac{11}{2} a^{3} + 14 a^{2} - 44 a - 104\) , \( 13 a^{3} + \frac{61}{2} a^{2} - 111 a - 253\bigr] \)
25.1-h2 \( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -\frac{3}{2} a^{2} + 2 a + 2\) , \( -a^{2} + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph