Elliptic curve isogeny class 25.1-b over number field 4.4.17600.1

• Base field: 4.4.17600.1
• Label: 4.4.17600.1-25.1-b
• 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-b over 4.4.17600.1

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

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[\frac{1}{2} a^{3} - 4 a\) , \( \frac{1}{2} a^{2} + a - 4\) , \( \frac{1}{2} a^{2} + a - 3\) , \( a^{3} - 8 a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 3\bigr] \)
25.1-b2	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 4\) , \( -8 a^{3} - \frac{47}{2} a^{2} + 38 a + 112\) , \( 15 a^{3} + \frac{93}{2} a^{2} - 72 a - 224\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph