Elliptic curve isogeny class 25.1-g over number field \(\Q(\sqrt{2}, \sqrt{7})\)

• Base field: \(\Q(\sqrt{2}, \sqrt{7})\)
• Label: 4.4.12544.1-25.1-g
• Conductor: 25.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}, \sqrt{7})\)

Generator \(a\), with minimal polynomial \( x^{4} - 8 x^{2} + 9 \); class number \(1\).

Elliptic curves in class 25.1-g over \(\Q(\sqrt{2}, \sqrt{7})\)

Isogeny class 25.1-g contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-g1	\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - 3\) , \( a^{2} + a - 5\) , \( 1\) , \( \frac{13}{3} a^{3} + 10 a^{2} - \frac{17}{3} a - 10\) , \( \frac{29}{3} a^{3} + 25 a^{2} - \frac{43}{3} a - 35\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph