Elliptic curve isogeny class 25.1-e over number field 4.4.17600.1

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

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

Curve label	Weierstrass Coefficients
25.1-e1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} + 3 a - 1\) , \( \frac{1}{2} a^{2} + a - 4\) , \( -36 a^{3} + \frac{215}{2} a^{2} + 171 a - 511\) , \( -\frac{2629}{2} a^{3} + 3994 a^{2} + 6263 a - 19029\bigr] \)
25.1-e2	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 5 a + 3\) , \( \frac{1}{2} a^{2} - 3\) , \( -\frac{3}{2} a^{3} - 2 a^{2} + 8 a + 14\) , \( -3 a^{3} + \frac{3}{2} a^{2} + 22 a - 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph