Elliptic curve isogeny class 3528.1-r over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3528.1-r
• Conductor: 3528.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3528.1-r over \(\Q(\sqrt{2}) \)

Isogeny class 3528.1-r contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3528.1-r1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 12\) , \( 6\bigr] \)
3528.1-r2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \)
3528.1-r3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \)
3528.1-r4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -38\) , \( 84\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph