Elliptic curve isogeny class 2704.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2704.1-c
• Conductor: 2704.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2704.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 2704.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
2704.1-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1838\) , \( 30638\bigr] \)
2704.1-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -18\) , \( 62\bigr] \)
2704.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( -2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph