Elliptic curve isogeny class 1648.2-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1648.2-c
• Conductor: 1648.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1648.2-c over \(\Q(\sqrt{2}) \)

Isogeny class 1648.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1648.2-c1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a - 3\) , \( -3 a - 9\bigr] \)
1648.2-c2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 17\) , \( 125 a + 155\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph