Elliptic curve isogeny class 721.2-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-721.2-a
• Conductor: 721.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 721.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 721.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
721.2-a1	\( \bigl[a\) , \( 0\) , \( 1\) , \( -150 a - 360\) , \( -1635 a - 3042\bigr] \)
721.2-a2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -5 a\) , \( -2 a - 7\bigr] \)
721.2-a3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)