Elliptic curve isogeny class 71.1-a over number field \(\Q(\sqrt{2}, \sqrt{5})\)

• Base field: \(\Q(\sqrt{2}, \sqrt{5})\)
• Label: 4.4.1600.1-71.1-a
• Conductor: 71.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}, \sqrt{5})\)

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} + 4 \); class number \(1\).

Elliptic curves in class 71.1-a over \(\Q(\sqrt{2}, \sqrt{5})\)

Isogeny class 71.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
71.1-a1	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( -a + 1\) , \( 1\) , \( -a^{3} + \frac{5}{2} a^{2} + a - 3\) , \( -2 a^{3} + \frac{9}{2} a^{2} + 3 a - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph