Elliptic curve isogeny class 25.1-a over number field 4.4.17600.1

• Base field: 4.4.17600.1
• Label: 4.4.17600.1-25.1-a
• Conductor: 25.1
• Rank: \( 1 \)

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-a over 4.4.17600.1

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

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( -\frac{83}{2} a^{3} - \frac{241}{2} a^{2} + 200 a + 573\) , \( \frac{837}{2} a^{3} + 1278 a^{2} - 1993 a - 6092\bigr] \)
25.1-a2	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} + 4 a + 1\) , \( \frac{1}{2} a^{2} - 4\) , \( -2 a^{3} + \frac{23}{2} a^{2} + 6 a - 60\) , \( -6 a^{3} + \frac{37}{2} a^{2} + 30 a - 86\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph